The Lima engines(Ford 4cyl) at notorious for running cold.
So what many do is to place something in front of the radiator, cardboard or ??, to block air from getting into the engine bay.
If the new t-stat is working the radiator should not even get warm so don't worry about blocking air flow.
The point of the thermostat is to stay closed until engine coolant gets up to 190degF, about 1/3rd on temp gauge, when t-stat is closed no coolant can circulate thru the radiator.
Once t-stat opens cold coolant comes in from the bottom of the rad and when it gets up to t-stat, t-stat should close again if coolant is below 190degF.
T-stat may run closed on very cold days and just slightly open on cold days.
Point being you shouldn't get wide swing in temp like that, 1/2 down to C, reads like t-stat is opening fully and then not closing when the cold rad coolant comes in.
You can also add "pipe" insulation to heater hoses, just on the long runs, it will help hold in the heat.
I would try blocking the air flow first.
Yes, engine generates the most heat when under load