Hi, heres a summary of whats happening. (Sorry PC restarted had to rewrite this)

I drive the car for about 20min or 15 miles then turn the car off it won't start or click like having a dead battery this only happens when its warm outside like 70+ degrees. Sometimes it'll start but won't be able to hold idle and die right away. I'm stumped on this and not sure whats going on any suggestions is appreciated.

-95 Celica GT 130k Miles M/T
-Spark plugs 1 year old Denso
-Spark plug wires bout 2 years old NGK wires
-Cap and Rotor 1 year old
-Fuel filter bout 1 year old
-No CEL's
-Cleaned the IACV 2 weeks ago
-New battery and POS/NEG terminals 1 month old
-Rebuild starter 1 year old

After waiting for about 15-20mins so pretty much letting the car cool down it would start right up with no problems.

check your fuel pressure, or your air temp sensor may be going bad

It's got something to do with the ignition. Possibly the coil.

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thats also deff. a possibility

Fuel pressure is good IAT sensor tested good also tested all the spark plug and wires. For the 94-95 5sfe the coil is external right ??

im goingto guess high resistance in the starter. i've seen it happen plenty of times. i'd say get it good and warmed up, shut it off, and do an amp draw test. if at all possible, take it off hot and do a bech test. to do it you hook an ammeter in series to the starter batt. terminal(30) and a charged battery. run the battery negative to the case. then connect a voltmeter to the battery and that will give you your voltage draw. run a jumper wire or remote starter to the starter batt. terminal(30) and the control wire(50). the starter should spin and the drive pinion gear will extend out when the jumper wire is connected or the button is pushed. check your amp dram and volt drop again. they should be no more than 90 amps. if more your starter is junk. i don't know the spec for volt drop but if its excessive (volt meter reading below 9v) starter is junk. if the starter doesn't spin, its junk. if everything else is good, then i would go through the coils and such. they are a less likely problem, but anything can happen...