1989 Supra idle

I have a 1989 Toyota Supra Turbo with 200,000 miles on it but it has a newer engine with about 50,000 miles. The car starts fine after sitting overnight but has problems starting 30mins to 2 hrs after I driven it. The engine starts but only reaches 500 rpms and then quits. It usually takes a couple of tries with my foot on the gas pedal to get it to start. I usually have to bring it to 1500-2000 rpms for about 15-20 sec to keep it from quitting on me in idle. After this process though the car runs great. What should I do?

Thanks!
~Bryan