In this case the maximum temperature is whatever the container wall (typically a neutron reflector of some sort) can withstand, while actively cooled by the hydrogen.
Large central inverters are typically actively cooled.
Everything from car engines to computer chips need to be actively cooled to prevent the build up of waste heat from damaging the hardware.
Jet blast deflectors range in complexity from stationary concrete, metal or fiberglass fences to heavy panels that are raised and lowered by hydraulic arms and actively cooled.
The Ge crystals are actively cooled with a mechanical system, and give an energy resolution of 2 keV at 1 MeV.
However, due to turbulent flow around the wings during re-entry, some parts of Skylon would need to be actively cooled.
LFTRs can include a freeze plug at the bottom that has to be actively cooled, usually by a small electric fan.
The heatsinks are actively cooled by a pair of 60 mm exhaust fans.
The engine also served as the primary heat shield, actively cooled by liquid hydrogen that was then dumped overboard.
Devices along the beamline which absorb significant power from the beam may need to be actively cooled by water, or liquid nitrogen.