I used to do this all the time.
Take the urine, put it in a gatorade or other plastic sealed bottle, and freeze it, if you really want to be slick, put it in like 10 different 5 hour energy sized bottles, and then freeze them all.
Before the test, I took it out, put it in the mircowave, and then took another (larger) container and put water in that, and then microwaved that, then I dropped my thawed piss into it so that way it kept it warm while traveling. Another option is to use hand warmers.
I know you said your doctor didn't check the temp, but believe me, when he grabs it to put the dip stick in it, if it's cold, or even cool to the touch, you're fucked. I had that happen to me. You want it to be warm, seriously.