Stalls, rough running, loss of acceleration power only when hot outside

This only happens when outside temp is mid 80s or higher. Car runs fine at first. After about 20 minutes it starts stalling, usually at a stop but has stalled while driving too. It always starts again, but begins to run very rough and has very little acceleration power. It also doesn't want to shift. The more you drive it the worse the problems get. If you leave it sit overnight, it's fine until the temp rises again. My mechanic has replaced the plugs and the crankshafts sensor. Most recently, the trouble code that came up indicated the PCM was bad, so that was replaced also. The problems continue. Please help!