I had something similar happen last weekend.My van has two cooling fans under the hood.One is for the radiator and the second one is for the ac condenser but both fans are mounted in one housing that mounts between the radiator and engine.I noticed a wire burning type odor and minutes later I saw smoke coming from under the hood.Popped the hood and I noticed blue arcing coming from the radiator fan motor.The fan would partially spin one minute and then stop the next minute.The fan had a slight drag to it also when spinning it by hand.Both cooling fans are supposed to run anytime you have the ac button pushed.Only one fan normally runs when the ac is turned off and the engine is above operating temperature.It also caused the radiator fan fuse to blow.I replaced the fuse then disconnected the wiring harness from the shorted fan motor til I could get the vehicle home and diagnose the problem.It was a shorted fan motor so I replaced the whole assembly,it was only $25more than the motor was

When you say your blower fan do you mean the blower motor that blows air into the cabin? If so this wouldnt cause overheating, and your air should still work on full blast. However if you mean the radiator fan, at idle conditions yes this would cause over heating. If both are working possibly check the hoses goig to the heater core, is it hot in one area then 6" ahead cool? There could be a clog causing overheating. Is the water pump leaking or making a grinding noise? Is it loose? You may want to replace that is your radiator leaking ? Or is there a crack or split in any hoses? Visual inspections are the first step

You would be wise to locate what and where the leak is and repair it .

" Smoke " could be an oil leak or a coolant leak , neither of which should be ignored .

Open the hood , start the car , let it idle until it gets hot and watch for where the " smoke " comes from .

Sounds like the A/C dryer ruptured.

My blower fan stopped running (again, but it restarted on it's own last time) a couple days ago. Then I started to notice a bad smell coming out of the vents even when they are "off". Today, white smoke was pretty well pouring out of the engine compartment. Is this all one problem? It does not register as overheating, which of course is my primary concern, but I can't handle the smell and neither can my five year old. What an I looking at for fixing this? Thanks.