I use the Fluker's brand heat pads for my female balls at home when I let them maternally incubate - since they get so hot, it encourages the females to lay off to the side of the pad, which works perfectly for those girls. For any other use (which doesn't require as hot of a hot spot), a thermostat is definitely needed to control the high temps a bit.
In response to the OP question, plugging the heat pad directly into the wall should not have caused a problem. As others have pointed out, they do require time to heat up, but sometimes moving the pads or peeling them off the tank and trying to reapply them can cause them to malfunction. If you like the flexibility of the heat tape but are like me and leery of the stuff, consider using heat cable instead. With some electrical tape, you can just tape it in place in any which way you want, and since it's totally enclosed there's virtually no risk of electrical fire. I'd still make sure you have a gap between the bottom of the cage and the surface it's sitting on (if you don't already), but the heat cable is one of my favorite heat sources.
Hope that helps!
-Jen