Ok, here's what I did...kind of gross but gets the job done.
Get a condom, clean it out well of all lubricant and what not. Cut a hole in the tip of it, then rubberband that shut. Get your buddy to piss in it, or a cup then pour it into the condom. Tie it off after it's filled then safety pin it to the inside of your boxers or whitey tideys or whatever, then when you go for your test...pull the condom out like it's your dick rip the band off and let it flow into their test cap. Either discard the condom down the toilet, or be safe and tuck it back in your pants then dispose of after you leave.
I did that probably 5 times and always worked like a charm. They always made me empty my pockets as well. Hope that helped!
Edit - As far as body temp, on the way to take my test I'd put the condom in aluminum foil, then right next to the vent on the floor with the heat on.