Your body is a bit like a Formula One car. They have to warm up the car first because all the tolerances are about when it’s working hard, not when it’s coming out of the garage, and your body is much the same.
Everybody’s slightly different – depending on how fast they ride, what their circulation is like, how hot and cold they are in general – but, on the whole, you shouldn’t be the right temperature in the first five or ten minutes of your ride.
In order to be the right temperature, you have to include the level of heat you generate while riding, and that takes about 15 minutes to happen. My theory is that you should go out and feel ever so slightly cold for 10-15 minutes, at which point you won’t sweat but you’ll generate the heat that makes you the right temperature when you measure the chill hitting you and the warmth you’re producing.
Otherwise you may go out and feel good for the first 15 minutes, but then you’ll start to sweat as you produce the heat, and you’ll catch a chill when that sweat comes into contact with cold air.
You can also wear an outer layer which is literally a 15-minute layer that you intend to take off once you’ve got up to speed and your body’s the right temperature. I don’t think I ever leave the house without an extra layer – a lightweight gilet or rain cape – that I’m either intending to take off, or to use as an emergency layer if the weather turns.