I figure I at least need to get them hot enough to burn off any germmies that are present
Unfortunately that isn't how that works. You need to heat meat to a certain temperature to kill bacteria that are common to the meat. You need to observe safe food handling practices (such as keeping above or below X degrees) to keep food safe from bacteria you introduce to the meat. Staph for example is something your grubby paws puts on the food, it produces a heat stable toxin. All the reheating in the world wont safe you from getting sick from it.
The middle of the meat may have been 172, what was the surface and for how long?