Chris,
The inexpensive thermometers will work fine. They may be off a few degrees, but they'll be closer than you can actually regulate the fire. Your palm on top will give a pretty good guesstimate as well. If you can hold your palm on the top for about three seconds before your skin starts to melt, you should be pretty close on temp.
I would try to elevate the grate so that the holes in your door are at or just below wood level.
You also need a lighter. I'll try to get a pic of the way I build mine and post it tonight. Basically take a piece of 1/2 pipe and drill small (1/16") holes all down the top. Cap one end, and attach a threaded hose barb to the other. A length of hose attached to a low-pressure regulator and then to a propane bottle. Drill a hole just below your grate level in the side of the firebox (center of box). Now, you load your wood, put the pipe in, hold a match while you turn on the propane and in just a little bit you have a fire and can turn it off. Beats the heck out of trying to light logs with fluid.
For $50, you should feel really bad and at least take the guy you got it from a nice Ribeye!