Thermal soakback is a phenomenon whereby a hot, operating engine transfers heat into the spacecraft, usually conduction through the engine mounts. I've only ever seen this problem discussed with RCS thrusters on satellites. The solution is usually an isolated or gridded mount. I have not seen this problem discussed with main engines on stages and wonder if the same measures are taken.
During the multi-hour coasts required by some orbit injections, heat from the engine (presumably) conducts through the mounts into the structure. Is it stopped by insulation in the mounts? Or is the heat allowed to conduct into structure?
Does the heat conduct through the tank insulation into the tanks over the course of the coasts? Or does the tank insulation effectively block it and keep it in the structure? Can this heat up and soften the structure during the coast?
Is this also a problem with lower stages? Does the conduction need a long coast to take place?