Yes, add the trans cooler, and have a safe trip.
My sister’s '96 Geo Prism did just fine hauling a trailer behind it with a motorcycle, and still survived many tens of thousands of miles later, when a taxi pulled a u-turn in front of her, finally sending the car to the junkyard.
BC.
You have lost your mind. How much did you spend on your education? Money a genius does not make.My apologies up front for my comments.
A 5x8 trailer loaded to the hilt with furniture could not only easily surpass the towing capacity of the Corolla, but it could also easily swing the light rear end of your Corolla around in the event of an emergency stop and cause a severe accident.
Remember, you not only have to go successfully, you have ot stop successsfully too.
I wouldn’t do it. I’d go with a U-Haul truck and a tow dolly and tow the Toy.
Pulling a trailer loaded to 1400 lbs with a Corolla will not difficult on flat terrain but might be a bit of a challenge going on long uphills with or without an auxiliary cooler. Stopping that weight is another matter, even on flat terrain. I suggest that you use a trailer with trailer brakes. In addition, most of the time a trip is uneventful but just one panic stop can ruin your whole day if the trailer jacknifes on you, another reason to have trailer brakes.
I would hope all this assumes the fully loaded trailer weighs LESS THAN 1,400 lbs., and I wouldn’t make that assumption. I would weigh the loaded trailer to be sure.
From the negative comments above it appears that several people have experienced the grief of pulling a trailer. Your situation has been a very common issue here. FWIW I considered buying some U-Haul stock when the market took its nose dive in 2008. But with regard to your question Mr Schsartz, the Corolla is not a good candidate to pull a trailer of any size. A 1,400 pound trailer is way beyond safe even if you took I20 and I10.
Stay off the cruise control once you reach the mountains. For the steeper climbs you’ll want to slow down even more (maybe 40-45), downshift to 2, and try to work on maintaining a steady throttle opening rather than a steady speed.
I would never try it–not in the summer anyway. After living in Arizona for 30+ years and making many, many trips from Phx to LA on I-10 with 5x8 U-Hauls (behind much bigger V-8 rigs than your Corolla), it is my humble opinion that your little rice-burner is not going to make it. But, I will be pleasantly surprised if you have a positive outcome. Let us know.
One thing not discussed yet (or maybe I missed it)
You have to consider the weight of the trailer EMPTY also…That trailer EMPTY weighs 900lbs…That means you’ll be able to load in only 600lbs of furniture. That’s part 1.
Now part 2…you also have to consider the TOTAL GVW of the trailer AND the car along with all the passengers and luggage and anything you put in there. It should be spelled out in your owners manual what that number is.
No way in h*ll would I ever consider what you’re doing…with or without a tranny cooler.
Your best bet is to rent a U-Haul truck and tow the Corolla behind it.
SELL THE FURNITURE!! So. CAL is overflowing with used furniture removed from thousands of foreclosed homes. Anything you want, pennies on the dollar…Yes, it will take you a week going through craigslist, Goodwill, Salvation Army and putting your household together, but the stuff is just piled up in the streets…Check out the L.A. area craigslist to see what I mean…
Having years of driving Semis across country under my belt, I would say this is penny wise and pound foolish. I have seen many disasters resulting from similar attempts. Put this on a trailer and pull it with a rental truck. That is the only safe option aside from selling everything and making an adventure out of it by driving only your Toyota and starting anew. Put the treasures with family or storage.
If you still proceed, keep this in mind:
The wheelbase of the Corolla is too short to safely tow a trailer of any size/weight down hills. It will push you down the grade; you will not be able to control the over-steer (sway) this will generate.
Have you considered the “tongue weight” at which the corolla is rated? At any, time will you exceed that? The answer is yes, at almost all times. The trailer hitch will push the rear bumper up and down, changing the dynamic of the car’s suspension, causing it to be difficult to control.
Additionally, by the time you calculate your fuel mileage; put on a tranny cooler and a trailer brake controller, you will have greatly exceeded your savings. Actually, the drop in mileage will pretty much kill your calculations. The wind is a persistant factor on fuel mileage reduction. Side wind more than head wind.
Geographically, there is no way to get to your destination without crossing multiple mountain ranges.
I estimate you will get about 3 to 10 MPG. You will likely run into mechanical difficulty somewhere about as far west as Wyoming or Utah. Your towing bill will likely exceed the value of your belongings. You will likely be washing dishes in some truck stop for years before you find your way to your destination.
Best of luck. Stay alive. Kill no one.
He doesn’t think that. He thinks the furniture will weigh 500lbs. He puts the gross trailer weight @ 1400lbs. Easy to lose the numbers here.
[b]One thing not discussed yet (or maybe I missed it)
You have to consider the weight of the trailer EMPTY also…That trailer EMPTY weighs 900lbs…That means you’ll be able to load in only 600lbs of furniture. That’s part 1.
Now part 2…you also have to consider the TOTAL GVW of the trailer AND the car along with all the passengers and luggage and anything you put in there. It should be spelled out in your owners manual what that number is.
No way in h*ll would I ever consider what you’re doing…with or without a tranny cooler.
Your best bet is to rent a U-Haul truck and tow the Corolla behind it. [/b]
Yes, you missed it. Multiple references to a 900lb trailer and <500lbs of furniture. Even his first post …and follow ups. You’re not alone, so don’t feel too bad.
I think that you can make it. You don’t have to worry. I hope you can! 
Goodluck.