heat soak, gone! lol
Yeah from the sounds of it I would think there is a larger problem. How about wires/plug/coil pack condition? I saw you had a tune up, but did you replace wires/plugs? Once those suckers heat up I would think it could cause problems.
Could shot tranny fluid also be an issues? <-- that might be out on a limb, but if the fluid is toast, it would probably cause issues after heating up for 10-20 minutes.