Runs good when it's cold, warm it chokes and dies

Hmm...........
1985..........
Probably carb? Automatic choke not working? Remove air filter and spray carb with cleaner, Make sure all parts move freely. With engine cold, check automatic choke position. Start and check function as it warms up.

sounds like auto matic choke problem try a manual choke

How many rpm's is it running at when you first start it up and it is running on the choke? Does it gradually start to idle back and then start to die r does it do it all of a sudden and dies?

When running with the choke on, it is on the high idle circuit of the carb, as it warms up the idle should slow down and then idle in the 800 rpm range in Park, 650 in Drive. This will be the low idle circuit range. This transition inside the carb will cover an idle air bleed hole in the venturi of the carb and lean out the mixture. If you notice that the carb smells gassy and black rich unburnt gases are coming from the tailpipe, the problem is located within the carb and requires a carb tech to do a rebuild of the carb. You could try a good carb cleaner like Lucas by putting it into the gas tank, in case you just got a bad tank of gas, but that is just a bandaid for a more deeply rooted problem. Get the carb rebuilt?

Cold starting problems from a carbureted engine? Bet if you get your choke adjusted right, it will solve it. If you can screech the tires, this Tercel may be worth saving!
Just get a mechanic friend or pay someone to fix the choke. Doesn't take a long time if you know how. If you've never adjusted or worked on one, it's not so fun. Hard to explain too. The choke plate or flap should be almost closed completely when starting. Soon as engine is cranked or running, the plate should open a small amount more, but still nearly closed. Then as engine warms, the plate should gradually open until it is completely open after about 5-10 minutes. The choke cuts off the air supply to the engine. A cold engine needs a richer gas mixture to run good, and most importantly to start easy.

Good chance it is not getting fuel, or enough fuel.
When the rig is cold, the choke is closed. As it warms up, the choke opens.
If the metering jets inside the carb are dirty, they may not be letting enough fuel into the barrels. You could also have a vac leak that is masked by the choke until the engine warms up.

Try putting your car in neutral, and then start it. Once it starts, put it in park, once you hear the engine start to choke out, rev the gas pedal, and see if it stays on. I used to have this problem with my '95 Ford Contour, I forget what the problem was. But, until you solve it, this may be your only solution lol. Maybe EGR Valve could be bad?

It sounds like it is getting too much fuel. check your fuel sensor. Your choke is sticking open. Buy some carb cleaner. Remove your air filter and spray the linkage to clean it up. Make sure it moves easy. Start your car up. the butter fly on top of the carb will be closed all the way. As the motor warms up this should open up gradually. If it doesn't you have a problem with the choke system and it is not letting air in as the motor warms up.

cold starting is assisted by the use of a choke or fuel enriching device
if it has carby , adjust the automatic choke device
if it has injectors replace the ambient temp sensor

Check out your cold start choke. It is designed to cause your fuel mixture to run "rich" until it warms up. It is basically a heat sensitive coil that reacts to heat from the exhaust manifold.

I would suspect fautly spark plugs.