Just to add a little confusion, I went through an intermittent stage of getting unwanted hot air sporadically; had one episode last spring, then a few since, and finally full-time unwanted hot air last week. Replacing the monovalve fixed it nicely.
The solenoid will indeed move even if the valve has failed; what goes is the rubber diaphragm that controls water flow. When it's torn, there's flow through to the heater core regardless of solenoid position. It's a cheap and easy job.
'97 SL500, 40th anniversary edition
'04 Olds Bravada (SWMBO's)
'06 Lexus ES330
'89 560SL (sold)
SL--Anything else is just a Mercedes.
(Kudos to whoever said it first)