When components get damaged by a "power line" surge, it usually is because current found a weak point between two things that are at different ground potentials and many times, the PSU actually has nothing to do with it aside from providing chassis ground through the power cable. Unstable or excessively out-of-spec outputs from the PSU (mainly caused by failing or under-spec'd output filter caps) are a whole other story and rarely related to what happens on the AC side.However, if there is a power surge, and the PSU doesn't handle it, then this could damage components regardless of temperature. However, this should be unlikely.
Fuse/breaker boxes offer absolutely no protection against surges unless you have a panel-mounted or snap-in surge suppressor. They protect against overload and in some cases such as the UK, also have RCD/GFCI functionality to protect against electrocution. Power line surge events are typically in the microseconds scale, orders of magnitude faster than the fastest household breakers. Unless the PSU is defective, power line surges have no effect on output voltages since they have no way to cross transformer isolation, which is why PCs practically always survive when the PSU goes bang due to weird stuff on the primary side such as power outages.If there is a voltage surge on the mains, then the fuse box would cut out. However, there is a very small delay, and so if the PSU cannot handle this, then it would give this overvoltage to the rest of the PC