You're in the UK, so I'm going to assume that's 5 degrees Celsius _ so still above freezing.
Where's your projector, in a fridge ?
Most specs stipulate that any projector should be kept above 15C.
IMO, I would use the projector to warm itself up.
If you use the temp in the room it would take longer then 10 minutes, something like over night before the components would reach room temperature.
Personally I don't think that's good for your machine.
Once the room warms to say 24C, the warm air holds more moisture.
This happens just from you breathing in the room.
Once you let the room cool to only 5 degrees, condensation will occur and you certainly don't want that, especially with a Sony projector.