I would disconnect the cable at the valve end and move the valve by hand.

If that shuts the heat off, you have some sort of cable problem,

If it does not, then you have a valve problem.

You could cut one of the heater hoses and instal a manual valve for winter and summer use. My friend's MGA had a little faucet right on the head to shut the heat off for summer.

My 1800 is incomplete (a basket case) but I have read about heat not shutting off in older Volvos, and my '64 544 has some heat coming out of the heater all the time.

For summer parades, I remove the soft hose from the front fender to the heater and attach a small 12v muffin fan to draw air from the passenger compartment and discharge it into the engine compartment.

That way, I can turn on the heater for extra cooling if needed.
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'96 855R,'64 PV544 driver, '67 P1800 basket case, '95 855, '95 854, the first three are mine, heh, heh, 485,000 miles put on 9 bricks

stick your head under the dash, face up and check to see that the cable sheath (corresponding to that lever) is still held by the clamp to retain it so that the cable in the sheath can open and close the valve.

If the sheath has "slipped", loosen the clamp, reinsert the sheath and reclamp.
I don't have my head under a dash just now, so there may be clamps at each end of the cable - could be either end.

If you can move the lever and see the cable at the other end of the sheath move the lever that actuates the valve, then most likely the valve is bad. That lever could probably use some lube in any case. (maintenance)

Just realized that this is an 1800 when I thought I was responding about a 122, so this may not apply. Some other 1800 fiend will correct me.