Seriously, thermostat. It is $4 for a thermostat and seal on RockAuto. Buy some new hoses too while you're at it. It's not fun doing repairs in the winter but after installation you'll be much happier.
Also,
this will look a lot better if you have a little time.
I'd say your time and money would be better spent on a thermostat and SNOW TIRES than duct tape. You can get a set of 14" Firestone WinterForces installed for $300 at Sears. It's cheaper than having a body shop straighten out your mangled core support and hood.
Sorry if that all sounded preachy, but a thermostat is going to be easier and more effective than covering your bumper with duct tape.