I don't know what they were like in winter, but I remember in summer all the drivers used to keep the sliding cab door open to get a nice breeze in. I suppose that would be against Health & Safety now!!
The cab has what is euphamistically called a heater, which also doubles as a screen demister. The passenger saloons also have heaters (the RM was the first London bus to be provided with them).
Neither of them work very well. The cab is draughty and, of course, in normal operation the lower saloon has a gaping hole at the back!
Mind you, the driver is pretty close to the engine! That must make giving some warmth to the driver a bit easier, and could explain Dean's comment about drivers leaving the door open in summer.
It must make it a bit noisy for the driver, compared with modern buses with engines at the back.
New Judges comments about the gearbox are spot on. I've driven both RT and RM (Routemaster) in service. The cabs were reasonably cosy in winter, if you got a good one!! Nearly always wore gloves though because the miniscule heater took quite a while to warm up.
Both cabs were very noisy because you were only about 2-3 ft away from the engine and there was no sound insulation.