The heating is controlled by the 2 solenoid operated valves just in front of the brake master cylinder (RHD UK car right?). These close when energised (under the control of the electronics behind the temperature dials) and spring open when current is cut. So you are looking for either failure of the control module or power failure which is failing to close the valves. Check fuse F7 (also supplies the revering lights) and the wiring around the valves.

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Mick J
'08 Chrysler 300CRD (MB OM 642 engine)
'95 E220 estate
'89 230TE (R.I.P.)