Why do opposing magnetic fields in the same core cause the core to heat up?
Your assumption that the core flux cancels out to zero is not valid because you don't have perfect coupling between L1 and L2.  If you had, then the inductance for the series-additive connected inductor should measure 120 (not 90) uH, because inductance is proportional to the square of the number of turns, and you're essentially doubling the number of turns. Likewise, you would measure no inductance for the series-opposing connection. Note that even if there was no coupling you would still measure 60 uH for the series-additive pair, so it seems  there is a fair amount of leakage flux. 

In the opposing flux configuration, the effect on the circuit is similar to replacing the coupled inductor with two separate inductors having much lower inductance values. As a result, the current ripple is higher, and the associated core losses are higher.