Bathroom ceiling bubbling, shower not getting that hot and leak from tray to ceiling below.. HELP!!

[Exchange230316]

Calling on wise mumsnetters yet again!
My bathroom ceiling, just above the rainfall shower head is bubbling
could that mean the fan needs replacing?
Have stuck two pieces of tissue paper and fan does seem to hold them plus a noise so seems to be working.
Fan seems to empty into roof. Showers are actually very quick and not that hot due to a possible leak from the shower tray that I am getting a plumber out for.
Does anyone know if shower has an internal device that controls temperature?
can anyone suggest solutions…
TIA

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The fan should vent to outside via ducting else you will get a lot of condensation on the nearest cold surface (which may the topside of the ceiling.

Mixer showers have a thermostat to prevent scolding which do go wrong so the cool temperature may be that or it could be limescale buildup on the guaze where the hot water pipe connects to the mixer.