The short answer: you have to work up to it and feel it out.
The longer answer:
Testing the grippiness of your tire must be done gradually, the idea is to increase lean angle gradually so that if the tire begins to slide there is some warning and opportunity to save it. The most pro coaches I have talked to on this advise gradually adding a little more lean at a time (corner after corner, or possibly even in the same corner if it is a long one) to feel out the traction, as opposed to just whacking it over to maximum lean and hoping for the best - because if you go too far too fast you will not have enough time to "sample" the traction and see how it feels, and know when you are approaching the limit.
Some tires will have a specific feel to them when they are cold: the Dunlop slicks, for example, have a tendency to make the bike want to stand up in the corner and that is a good indicator that they are very cold. The carcass is stiff and reluctant to flex so when you lean into the corner it resists and sort of pushes the bike back up. Some other tires just feel a bit "wandery" in the corner, like they are sort of weaving around slightly, instead of feeling planted. If you have ridden in rain or ridden dirt bikes in the mud, you can recognize the feel of little slides, and little slides like that are your warning that you are at about the limit of traction for the conditions and the tire needs to warm up more before you can lean over any farther.
It is a great exercise, when opportunity presents (winter is coming!) to pay VERY close attention to how your tires feel when stone cold, to develop a sense for it with your own bike and your own tire brand/model.
It is difficult to quantify how long tires will take to warm up because it depends on tire type, air temp, track temp, wind conditions, how hard you ride, etc., so the best solution I know of is to feel it out carefully.