Here’s a quick tip you can use to check if the valve is stuck without removing it:
With the engine warm, turn the heater knob from cold to hot.
Watch the hoses going into the firewall: one of them should get noticeably warmer when the knob is turned to hot.
If both hoses stay the same temperature, or the “hot” hose never warms up, the valve is likely stuck closed.
If the hoses stay hot all the time, it may be stuck open (not your case, I believe).
Basically, the valve simply opens or closes the flow of hot coolant to the heater core, so hose temperature is the easiest check before dismantling anything.
This saves time and confirms very simply whether you actually need a new valve.