On the hot weather on Monday/Tuesday it does not look promising - from the Southern site:

Southern Services

Southern services will also be significantly revised and more detail about the changes that are needed will become available over the weekend.
Southern metro services between East Croydon and London Bridge via New Cross Gate will not run.
Southern metro services between Caterham and London Bridge via Tulse Hill will not run.
Gatwick Express services will not run but Southern services will run in their place making extra stops.