Does anyone know at what temperate Polystyrene burns? I have some in the
base of a shower that is being installed and there is a chance that it
will
touch a hot water pipe. Is it likely to burn at this temperature?

Absolutely not. Polystyrene can be used to insulate hot water pipes.
Generally speaking, it is best used below 70C, so is more suited to DHW
applications (such as your shower), rather than central heating systems.

Christian.