It is normal for them to tighten up when hot.
My '18 TG just crossed the 20k mark and I've done nothing to the belt. From new it seemed very tight to me and I checked it when it was stone cold. I had two different techs look at it and they said it was A-OK and that it would stretch a bit with some miles on it. With 20k it does not appear to have stretched a bit as it is still tight. But I've inspected TGs of several different friends and are all tight. 3/8" ain't much at all and it is darn difficult to get an accurate measurement. . . and it looks a bit intimidating to me to adjust so I'm just going to leave it alone.
It's a heck of a lot tighter than I ever ran on my two wheelers but perhaps I didn't know how to adjust them properly and ran them too loose. But I never had any problem and put well over 60k on them all and over 80k on two of them. Honestly don't know if it really is all that critical as long as it's not so loose that it can slip.