A solution to the original question.
Start the car with your 1st key. Get out, goto the passenger side, get in, lock the doors with the central locking button, open the passenger door again (I can't remember if this unlocks both doors and boot though, if it does, then press the lock button whilst the passenger door is open, one of them works).
Then get out and lock the door with your key.
I did this a couple of times when I had a few minutes to spare in the morning and didn't fancy getting in a cold car. I live on a very quiet road so didn't (and don't) consider it a risk.
But with regard to the whole thing. I just throw some hot water on the screen. Though the other day when it was -8 according to iPhone, by the time I'd jumped back in the car the water was freezing from the bottom of the screen to the top.
Reminded me of 'The Perfect Storm'