UTH's take time to heat up, what makes you think that yours is broken?

Plugging it straight into the wall isn't going to hurt the UTH, but doing so will end badly for the snake. Without a thermostat to regulate the UTH they can and will get 130 + degrees (more than enough to kill a snake). That said don't bother with the repti-temp, as it is junk. The Zoo-Med UTH's are fine, but their thermostats are not.

Here are some good thermostats:

Budget: http://www.amazon.com/gp/aw/d/B000NZZG3S

Mid-Range: http://www.reptilebasics.com/ranco-etc-111000-pre-wired

High Quality: http://spyderrobotics.com/home/products.html

A thermostat is not optional for using a UTH.