Go in for a check up to see what the mechanics say but I think it could be your battery or alternator. Oh yea what make, model, and year is your car?
get the head seal checked. also the water pump.
The previous answer about the battery or the alternator is good. Also check the battery connections as this could also be an issue. If you have not had your timing belt changed then you may want to check your owners manual. You do not want your timing belt to go - it will kill your engine.
Sounds like a fuel or timming problem…..is fuel injected or carb? does it have good power when it is not stalled? often it is a dirty injector or throttle body. the over heating is another problem i think….check your belt condition and coolant level….also check for scaling in the radiator….I would try running a fuel cleaner through the fuel tank…it is easy just add it when you fill up and it will try to clean your inj/thr body. it is NOT your alt or battery…if it were it would not start again after it stalled. With the info provided that is all i can say right now…
It is probably the fuel filter trying to stop up. Or your fuel pump is going bad. If it is fuel injected could be injector problems but I would check the fuel filter and fuel pump first. If it is overheating check the radiator it could be blocked from bugs. Check the coolant .
If your car starts back up after stalling it is not the alt. or battery. The engine is not getting enough air or fuel at a idle buy the sounds from what you are describing. These things are controlled by the computer system. You need to take it to auto technician and have him/her test it for errors. A tune up does not solve most of todays problems like they did before computers.
You didn’t say what kind of car this is. If it’s an early 80’s to early 90’s General Motors car (Chevy, Pontiac, etc.,) with an automatic transmission, this was a somewhat common problem. There is a switch, or valve (TCC or torque converter clutch solenoid,) that basically causes the automatic to have zero internal slipping when at cruising speeds. This is fine, and saves gas mileage. Cars still have the same kind of set-up today. The problem with these GM cars, was that as the transmissions wore internally, little flakes of metal were attracted to these solenoids in the transmission (due to magnetized metal on the solenoids,) which eventually caused the solenoids to stick in the locked up mode. Again, it would be fine driving around, but when you come up to a stop sign, and apply the brake, there is no internal slippage allowed in the transmission due to the malfunctioning solenoid, and the engine dies. It is much like coming to a stop sign with a stick shift car, and never pressing down on the clutch pedal. The transmission can’t release from the engine, so the braking of the car kills the engine. It will start right back up, buck a bit until your going a few miles and hour, and will be fine until you come up to another stop sign. I don’t know if this is a common problem in non-GM cars, but seems likely. I hope this helps.