Hi everybody!
My 2001 toyota camry has been overheating. I noticed that the cooling fan on the passenger side isn’t spinning, and replaced it but it still overheat. Then I noticed that both fans spin slow when the AC is on, but do not spin when the AC is off, even when it’s overheating. I played around with the relays and found out that if I unplug the no. 3 fan relay, both fans spin fast when the AC is on, but still won’t spin when AC off. But driving with the fan no. 3 relay unplugged still makes it overheating. I’m kinda stuck right now and been using the heater when driving to ease up the overheating. I wanted to try and error by replacing the relays and coolant fan switch to see which will help, but haven’t done yet because the staffs at the autoparts said I wouldn’t be able to return those relays and switch once I walk out the door 
Is anyone familiar with this problem? Please help me out. Thanks!
Thanks for your reply. I’ve found out that the thermostat was stuck close, thus the hot coolant cannot go through the inlet hose where the fan switch is that it won’t be hot enough to turn on the fan. Funny thing is that both the cooling fan motor and the thermostat went bad at the same time that brought me a lot of confusion 
Glad you got the problem solved. Suggest to never run engine with relays removed. Relays are very robust, not a common failure item. There may be serious unwanted side effects if relay is removed and engine is running. In the circuit above the least robust parts I’d guess would be the two switches on the right.
My guess for why you had both a faulty thermostat and a faulty fan motor, not a coincidence. As the thermostat started to fail, coolant overheated, and this caused the fan motor to be spinning more than usual, which caused the motor to overheat and fail.