The 12 inch diameter hole is a convenient size because it lets you easily drop in a wort chiller through the top (many of them are 10 to 11 inches in diameter), plus it removes most of the domed top end of the keg giving good visibility and access to the deep and narrow shape of the kettle, and it is a common size for stainless steel boiler lids. For example, I have two 8 quart stock pots in my kitchen that have 12 inch diameter lids, so they both would fit a keggle with a 12 inch diameter opening. (Unfortunately, the opening in my keggle is 11.5 inches).
I think that's the only reason why most people shoot for a 12 inch diameter hole. You can really make it whatever size you find useful. If you use a keggle for fly sparging later on, a bigger hole that is almost the diameter of the interior of the keggle will allow for more even coverage. (I'm guessing on that part, as I haven't ever done it.)
Thermostat I haven't heard of (but I don't know that much yet). Dial thermometers are commonly installed in keggles. I don't have a thermometer in my keggle. I want to put one in, eventually, but I'll need someone to weld me a fitting for it, or drill a hole and use a weldless fitting. Right now I take temps with my digital meat probe.
Go ahead and start a new topic in the future. I personally think it best when the subject line of a post bears some relevance to the content.
