Can you make birds start moulting like by changing the room temperature would they go into a moult then? I find my birds sometimes ended up moulting all the time from change in temperature and now the house temperature is always the same.

There are a lot of different influences on molting, and it probably varies by species. Outdoor birds tend to molt just once or twice a year, but sometimes indoor birds will have a series of small molts instead of one big molt at longer intervals.

And is this caused by temperature

I think temperature can make a difference. Many wild birds have their molt at a specific season, and temperature changes are one of the signs that the seasons are changing.