Misfire or something after warm up

Hey guys, i just picked up my first z car! It is an 86 300zx. Before i start going on about other things lets get to the problem. I bought this car knowing there was this problem but for the life of me i can not figure it out and being in highschool, I Dont want to go and spend money trying to find the problem as I don't have a ton of funds. well here's the problem and it is very weird. Ill start the car up while its cold and for about 20 or so minutes will be a blast to drive and have full power like nothing is wrong but once it warms up it almost loses all power. It will continue to idle though it is vvery low. it seems to have a miss or something becuase i will try and give it gas but it bogs down and even in neutral trying to rev it, nothing will happen. now that might seem like a common problem but here is where it gets weird. once it starts doing the miss i can turn off the car and instantly turn it back on and it is perfectly fine for a couple minutes and then the process just repeats. Also if it starts to mid and you give it full throttle it will eventually get going but only at full throttle. the guy i bought it from couldn't figure it out either and thought it was injectors or coil pack but with it only happening when its warm makes me think it isnt the injectors and with it basically fixing itself for a little if u turn off and turn back on the car just really puzzles me. I work at a shop and have talked to them about it and they can't really pin point the issue as it is so strange if anyone can give me any info on what it may be or if anyone else had this problem how did they fix it. Its a blast to drive and runs really well until its warm and i just want it all to be working good. ANY INFO WILL HELP
please and thanks. jack
edit: i have tried and search many forums and can't find anything on a problem like mine feel free to reroute me if you know of a thread with these problems