Dan,
I had occasion to check out the speed which my temp gauge changed on my ride into work this morning. I left my heated garage (60 deg) and left for work, and within 3 minutes the temp was registering 38 deg, and within 5 minutes it had settled on 34 deg, which was what my thermometer at home said was the actual temperature.
So by my super-scientific measurements, approximately 5 minutes to normalize to the actual outdoor temperature.
YMMV (and probably will depending on the temperature variation, whether you're going from hot to cold or vice-versa, etc.).
Ray