As a tangent while looking for numbers for the L/D ratio impact on entry profile, I came upon this site which seemed to favor skipping reentries in almost all cases. Reading further, I realized that it's not dictated by fundamental physics and is intentionally designed in the trajectory planning.
The Wikipedia page gave the following reason for using skips:
to achieve greater entry range or to slow the spacecraft before final entry, which helps to dissipate the huge amount of heat that is usually generated on faster descents
This doesn't make sense to me, because by dipping further into the atmosphere (to generate more heat, in order to get upward velocity), the vehicle would generate more heat, which means that the time spent outside of the atmosphere would merely be compensating for that heat generation. It's not obviously better on-balance. In the long run, you still have to generate the same time-integrated amount of drag...
Can someone give a complete argument as to how skipping reduces the thermal load on the craft?