Cooking a ham a second time

Somebody's going to tag this question as a "duplicate" pretty soon (as we have a lot of questions that address this sort of food safety issue before).

But let me just say briefly that according to standard food-safety recommendations, this is NOT safe. Below around 130F, bacteria will grow in food, and many kinds of harmful bacteria grow the fastest in the range around or a little over 100F, which is where the center of this ham spent a lot of time. Until the ham gets over 130F, those bacteria will not start to be killed off.

When you took the ham off the grill and put in the fridge, it will take the center a long time to cool back down, during which time it will grow even more bacteria. And then tomorrow to heat it back up, it will likely take a few more hours, during which even more bacteria will grow. It may end up spending 6-8 hours total in the "danger zone" where bacteria grow rapidly. If the ham reaches a higher internal temperature for a longer period, that will kill off the living bacteria, but with so many hours in the growth zone with heating and cooling and reheating, those bacteria may leave behind toxins that won't necessarily be destroyed even with higher heat.

All that said, there are fewer bacteria in the center of a large hunk of meat, and cured meats with high-salt content, etc. will slow bacteria growth. So, it's possible (even likely) your ham will be okay to eat. The problem is without knowing how it was processed (and under what conditions), how long it may have sat at other times before you received it at temperatures that would allow bacterial growth, etc., you can't know whether it's safe. That's why food safety organizations have strict recommendations, and they'd say your ham may be unsafe now.