This sounds like something is warped and it gets worse with heat. Most new clutch installs recommend that you take the flywheel off and get it resurfaced. (Resurfacing involves mounting the flywheel on a turntable and having the surface ground flat to remove the hardened high spots) Though after thinking about this I don't think that's the problem.
Did you check to see if the clutch disc moved freely back and forth on the input shaft? Was the clutch disc installed the right way? (most are marked "flywheel side") Were all the clutch release fingers at the same height once the pressure plate was tightened down? Were the pressure plate bolts each tightened down a little at a time till the pressure plate was tight against the flywheel?