Instead of a center punch, what you need is something called a "Transfer Punch". They come in sets from around a 1/16th od to 1/2 inch. The trick to them is that their body is the exact diameter of the hole and they are tipped with a short point that will mark the metal.
To use one, all you have to do is set the t-stat housing back into position and use the one good bolt to secure it. It has to be located just exactly as it would be if there were the two bolts doing the job. Then you use either the 3/8ths or the 25/64ths t-fer punch, depending on which of them is snugger in the hole in the ear of the housing. The housing acts as your guide, you set the punch into the hole, make absolutely sure everything is exactly where you need and want it to be, and then just use a regular machinists or ball pein hammer to apply a good solid tap to the punch, same as if you were marking metal with a regular punch. Once you do that, remove the punch and the housing and check your work.
If you have a good well defined dimple showing in the stump of the bolt and it looks to be centered correctly, then go ahead and run a pilot hole through the corpse of the bolt. Do Not use the stump of the bolt as a gauge or guide to tell you if the punch mark is centered. Remember that the hole is threaded and it can appear like the punch mark fell off center but is, in fact, an optical illusion.
Once you run that pilot hole, and be careful not to lean on the drill too hard or you might be trying to extract a broken drill bit along with the bolt, you can go bigger on the drill bit until you are happy, or as close to the threads as you care to be, or you have removed enough that you can pick the rest out using suitable tools for the process, or may be able to use an extractor but be careful with them with because they can be brittle and break too, Or, you can use the pilot hole to guide your left hand bit, and any good tool house should carry them, and try for the extraction that way For the left hand bit, you want High Speed Steel, abbreviated, HSS, to show on the shank of the bit. Don't go with CSS, that is Carbon Steel and they are soft and die easily.
Again, if all else fails, like has been already mentioned above, there is the option of gutting the hole of its threads and installing a Heli-Coil. They come in kits, usually with a special drill bit if needed, and have excellent instructions as to how to go about making the repair.
This next part is just me and not something I would generally recommend but for the helicoils that I have installed, if possible, I do two things. First I spray the site with a generous coat of Locktite Clean and Prime. The C&P contains a catalyst that will assist the Locktite to set. Then I coat the insert with a very stingy amount of Locktite Red; just s small drop or two, no more, and immediately install it in the guide sleeve and use the insertion tool to screw it down and into position. Remove the insertion tool immediately and stop. The instructions will tell you to use needle nose pliers, or a screwdriver or pin punch to snap out the tang on the end of the h-coil. For myself, I wait a day and then snap out the tang. The day is me wanting to make sure that the Red sets completely before I go hunting for that tang. Retrieving that tang is a PITA. If the hole is blind then you can fish it fairly easily but if the hole is open to the water jacket and you drop it into the chamber below the t-stat then you have to do a little fishing around in there to drag it out into the open and grab it.
Why all the hubbub about that little sliver of metal? Well, if all it did was to drop and sit there then all might be well. If coolant circulating happens to grab it then it can end up in the water pump and really ruin your day.
Nick