Can I be too cool?

[tucsonjwt]

I had a leak in the water pump in my 454 C20 so I replaced the pump with a new Delco pump, found out I needed a fan clutch and replaced that with a Delco clutch ($$$), found a small leak in my 2 year old Ready Rad radiator and had that fixed, replaced all of the hoses and belts, and then took it for a short test drive.
No leaks, but the temp went up over 220 degrees after just a few minutes. So, I replaced the old thermostat (looked like it could have been factory original style) with a 180 degree thermostat from NAPA, and after a 10 minute drive in town it only got up to about 165 degrees. It was about 99 degrees outside, so it was quite cool for Tucson in July.
Is it possible that my big block could run too cool. I can't think of a problem with that, since I have no computer controls on this old truck, but I thought I would submit this question to the forum experts. For reference, this truck never got up to the 200 degree range in the past (stock thermostat should be 195 degrees for this truck). As I recall, the highest temp I got in the past was about 185 degrees, assuming the stock temp gauge is accurate.