A useful temperature gauge in a wristwatch is an illusion. Tissot sells watches with temperature gauge. Last time I looked in a manual it said that you need to take the watch off and let it sit for about 15 minutes before you get a fairly accurate measurement. It seems they use the gauge for compensating temperature influence on the oscillator and allow to display it as one more gadget.
A thin watch might be quicker with the reading.
Maybe designing and building a watch like your ideal watch could become a project for the ETS community.