Engine Overcooling?

Since the air temperatures have cooled off significantly I am now experiencing temperature fluctuation with my 93 Cobra that I've been restoring. New pump, thermostat (stock 192), 3 core aluminum radiator, HD fan clutch (CJ pony parts), and a/c condenser is removed. Valance is installed along with the factory shroud
The temp gauge regularly fluctuates between the line right below A (sometimes below the line) and M, and I've noticed when I come back from a drive i can touch the top of the radiator! Heater blows hot air.
Is this a case of over cooling and the thermostat keeps opening and closing? Best advice? Block air flow?
15463105456208662537972226578696.webp
 
I would say the thermostat is doing its job by regulating engine temperature. If the engine isn't getting hot enough to open the thermostat, it won't let it flow to the radiator so the radiator cools off. Your heater core is a small radiator, and when it's cold outside and your heater is on, it's probably enough to keep the engine from overheating.
 
Grab a inexpensive manual temp gauge and mount the sender in the thermostat housing if you can, zip tie the gauge to a wiper arm and go for a cruise, that should tell you whats going on temp wise.