Hot G day

Hi, just wondering whether this is normal, driving the G yesterday ( went to Brooklands for a BMW 2002 meet and hillclimb) obviousley it was a hot day , temperature fine whilst on A roads but whilst in traffic for 5 mins or so temp crept up to the 3/4 mark, as soon as I got going again temp back to normal halfway. No outward signs of overheating ie no steam or water leakege and the fan appeared to be working fine, is this normal behaviour or do I have a problem. Also I recently had an alrm/immobiliser fitted, the fitter concerned told me the system could not operate all the doors due to the central locking at drivers door, suggested I needed a new motor? strange because central locking worked fine before, bit of a pain because cannot lock doors from inside, and need to lock drivers door first , then press alarm, does this sound familiar to anybody.

love Frannie