2002 Jeep Liberty Sport Overheating

(I see the options to “Select a Vehicle Make” and “Select a Vehicle Model” but I am not getting a drop down option. This may not matter but I wanted to go ahead and write this to ensure that my post would not be removed for “illegitimacy.”)
So I own a 2002 Jeep Liberty Sport with a 3.7l engine and I have had overheating problems with it recently. I am not to knowledgeable when it comes to vehicles so I figured I would come to a vehicle community in the hopes that maybe someone could point me in the right direction.
I am starting college in less than a week and I need my vehicle to be in good working order. It has been overheating after I have been going slow down dirt roads, going no more than 30mph. It has overheated three times, and each time is has overheated the engine dings and right after it dings I start seeing steam from the coolant that has leaked out of the tank onto the motor. The coolant is boiling at this point which leads me to think that there isn’t a good circulation going on, but then again I don’t know much about vehicles so I could be wrong in my thinking. Right when I see it getting into the red I pull over and shut the car off to keep the engine from getting any hotter.
Despite this, when I am going down the road, say 50+mph, it is fine. The only times I have problems is when I am going down dirt roads or after I have been on them and am now back on paved roads.
It is worth noting that it isn’t leaking coolant. The only time I found a leak was the most recent time it overheated and I saw a thin mist of coolant spraying from the radiator, but I think this was from it getting so hot and so much pressure building up that it cracked around the molding of the radiator. So other than this little leak in the top right corner of the radiator, coolant is not leaking from the lines.
I think it could be a few things:

  1. I think it could be the thermostat. My dad thinks that this is the problem to, but right now I know it could be a number of things so I’m not sure that this could really be the problem.
  2. It could also be the water pump. Like I said earlier for some reason it might not be getting good circulation so maybe this is the problem.
  3. The fan could have gone bad. I am not so certain on this one as the first two because a few days ago I was testing to see if the fan worked and I put the car in neutral and pressed on the gas pedal and I got out and looked at the fan and it was spinning and it looked like it was spinning normally.
  4. The fan wire plug could have gone bad. I have thought about this and thinking that maybe while going down the dirt roads this plug jiggles just enough to lose a proper connection and could have blew itself.
  5. Lastly the other thing I can think of it being is the radiator. I know I need to replace it anyways because of the little hair sized crack, but is there a possibility that it is causing the problem?
    Again, I don’t know much about cars. I have a general idea of what problems I could be having, but I am not even sure if the problem is even any of the 5 things I listed. I know that as readers you won’t have as much of a good idea of what the problem is without seeing the problem yourself, but I’m not willing to cause the vehicle to overheat again just to get a few pictures or a video to attach to this post.
    So, with that said, I suppose that I am asking people who know more about cars than me to see what their opinions are about the problem I am facing, so just some ideas would mean a lot.
    I have watched some videos recently to get a better idea of the problem, and I think the engine layout for Jeep Liberties from the 2002 model up to the 2006 model are almost identical, so if any of you have worked on a Jeep Liberty with a similar problem to me from within this time gap then your post would be great.
    As for the thermostat I might as well go ahead and replace it because I know they don’t cost to much, but as for the other parts I am not sure I want to go spending money on replacement parts and it end up I don’t even need them.
    Thank you to all who have read my post, and any response will be greatly appreciated.

When the engine is running hot check to see if the cooling fan is running on high speed, the fan motor or fan relay could be failing.

Next time I take it out to drive I’ll check that. But Usually when it is hot, as in it being in the red, I turn the engine off to prevent it over heating to the point where the engine ceases. But last time I had it stuck down a dirt road I turned the engine on for a few seconds while it was hot and the fan wasn’t blowing, so that very well could be what is causing it, and that would make since. One thing I forgot to mention was that I had to change the motor relay fuse because it had blown, so if the fan relay is failing then I suppose it would be trying to take to much current and cause the fuse to blow in the first place. I checked the new fuse I put in when it overheated the last time to make sure it hadn’t blown and it didn’t, so I’m not sure if this points to it possibly being something else.
Thanks for the reply. I wasn’t even thinking about it being a fan motor I was thinking of it being the fan itself, so if this is actually the cause then this could very well save me a lot of money.
Also, I have just one question in regard to your post. If the fan isn’t running or is running slowly, would the most definitely mean that it is 100% the motor?

Are you sure the coolant level is full and purged of all air?

If the coolant temperature sensor for the fan is not in the coolant, it won’t know your engine is hot enough to turn on the fan.

Seems like a pressure test is in order. If the crack in the rad goes all the was through, thre cooling system won’t build pressure and it won’t cool as well. It may also tell you if there is a bad head gasket because if it is not leaking at the crack or anywhere else you see, might be a hesd gasket.

If you replace the cracked rad do the T-stat, too. I would replace the fan relay as a matter of course. They are cheap and easy to replace.

Thank you all for the replies. I wanted to make an update on the situation. Earlier this morning I put the Jeep in neutral and revved the engine to have it get hot. I turned it on once and gassed it and turned it off for a little while, then I turned it back on and did the same thing. The first time the fan was blowing, and then the second time it wasn’t working at all. After a while the water I had in the coolant tank as a temporary coolant was boiling, yet the gauge wasn’t showing the engine was overheated.
A few minutes after I turned the engine off a mechanic that comes into the store I work at looked at everything. He had me turn the engine on and he was looking at the fan. He started hitting it and then it started blowing again. He said that the biggest problem, if not the only problem, was that the fan was bad, which made it just stop working at times. I am having him replace the fan and I’m hoping all is good from there.
I think it is worth noting that the coolant tank was basically empty when I started checking it out. I filled a jug up with water and put it in the tank and revved the engine. I looked at the tank again while looking at the fan and for leaks and the tank was empty. I looked to see if it leaked onto the ground but there was not puddle of water, so this leaves me to believe that the water pump and thermostat are doing their jobs and getting the coolant flowing.
I saw where It_s_Me stated that air could be in the lines and is keeping the overheating from being read. I think that this might be what caused the engine to overheat without warning while I was testing it this morning. Once I have the new fan I will purge the lines and refill the Jeep with a new jug of coolant.
Again thank you everyone for your replies. This community has helped me greatly and I send you all my best regards.

The blown fuse was an indication that the fan motor was failing.

The radiator fan clutch may be faulty.