Q: Lack of heat from vents. New thermostat or coolant flush?

One morning, the heat suddenly stopped working on my way to work. Brining it into the shop, they disconnected wires and cables from the valve that allows coolant into the heater core, and it miraculously started working again. A week later it happened again, but I can still get some heat out. The thermostat on the engine when fully warmed up shows under halfway between L and H (if it was a clock with L=10, and H=2, it's at about 11:30, little lower than 12/half but noticeable). The heater valve is moving it's full range of motion, I am going to top off the coolant reservoir (it's a little above Minimum, I'll put it to Max). I had the water pump replaced within a year ago and rear heat works.

My next thoughts are it's a partially-open thermostat (which I bought a new one and may put it in if the coolant addition doesn't fix it) or some blockage in the lines, or even possibly a sensor or Climate Control panel. Any other information to help determine or troubleshoot I'm all ears. Thanks!

My car has 118500 miles.
My car has an automatic transmission.