When you install your thermostat, the hole goes at 12 o'clock.
While I would never discourage anyone from buying another tool, and dremels are extremely useful, are you really saving that much money by purchasing an automotive thermostat? You don't own a set of twist drills and a drill motor? Is that humanly possible?
Should you drill your hole, how will you install a little clapper (ok,
@Roger. called it a jiggler) to keep it clear?
Speaking of these, it sparked a memory - an oldie but good one. Pardon my digression, this is a serious answer to you post with a pause for some amusement.
Other posts notwithstanding, I had a thermostat failure. There was sufficient coolant in the system, and the stat started sticking - it took a long time for it to open and eventually would not close. When I pulled it, there were scratches on the center 'post'. Larry said these were evidence that the stat was failing. Replacing it (though I muddied the waters by also replacing the o-ring, a few hoses, clamps and coolant) solved the problem. I say 'muddied the waters' because if you want to determine a cause of failure, you have to change only one parameter - though one could argue that its hard to describe how the o-ring could be the cause of overheating.