97 cavalier starts and runs ok from a cold start after a few minutes of warm up it starts to run rough and miss. If i try to drive it it will start out ok but won't shift automaticly but shifts fine m

Could be spark or fuel.
Weak or worn spark plugs, weak coil, dirty injector, and so on.

Here are the most common causes of idle surge, rough idle esp when cold and stalls at stops, slow idle speed, erratic idle speed, rough idle and engine hesitation (and other problems), it is in most cases the idle speed control air-bypass valve and or throttle valve and upper intake, these area's get full of gunk and combustion residue over the miles and cause idle issues (stalls, low idle) like yours, Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake.

Sounds like it needs a new thermostat.

Buick 97 lesabre, runs rough when warm

Sounds like an engine sensor problem (could be one of several) - start with an error code (DTC) check with a good code reader and follow up if there are any.

The most common problem is a partially clogged injector. They should be cleaned about once a year. Also the coil housing is known for shorting out between cylinders on your engine. The reason that its worse with the AC on is because the AC compressor is adding a load to the engine. You should probably take it to the shop and have it diagnosed soon before the misfire damages the catalytic converter.

check the vaccum hoses to make sure none are off and check the timing and also the drive belt and also check the vacuum hose behind the throttle body

Check the fuel pressure when the vehicle is cold and compare it with when it's hot.Also check the fuel return dump valve , that this isn't returning too much fuel.

016 Engine Misfire Misfire Scan Data Find someone who knows what scan data is an knows how to use it .Intake manifold vacuum leak .
Rough Running When Cold GMC Yukon

Its because that the engine is very cold, try to worm it up more time before you start driving.