You do as you said, you set the thermal stones next to a fire until they turn bright red - the larger/hotter the fire, the warmer (until it's max) the stone will get. When you pick it up into your inventory it will slow down the rate at which you freeze when you leave your fire/source of warmth.
The stone will slowly lose it's warmth over time (at a constant rate) and will need to be recharged by placing it back by a fire. If it turns grey it has no warmth left. Having multiple thermal stones on you does not change anything vs having just the one. (If anything it is inefficient and wasteful). Having multiple would only really help if you kept one warmed by the fire to swap out for a cold one when you got back if you needed to run back out to explore etc.
Other items that help reduce this rate are warm clothes such as beefalo items, and wilson's beard.