Not quite sure what is meant by Ambience but I assume it means the unit is in Standby mode.
What controls it's On/Off status is a thermostat. Older electric heaters' thermostats were of the electro-mechanical type nl a heat-sensitive bi-metal strip that simply flexed and triggered contacts to switch on or off depending on the heat it is exposed to. They are set at the factory via a small set-screw and usually sealed with some heat resistant 'glue' or paint.
Thie problem may lie here: Contacts have been carbonised over years' of use that they are no longer making proper electrical contact - even though the bi-metal strip is still flexing due to its temperature. Or the contacts have been so eroded that they are no longer electrically reliable.
When in standby and the ambiant temp drops, the contacts should be in contact allowing the heating current to flow. This you can easily test using a multimeter which should read almost zero ohms across the contacts. [after unplugging the heater first of course].
Test whether the strip snaps open & close when you turn the setting knob. Inspection of this simple mechanical mechanism will usually reveal the problem. If the contact points have been carbonised but still have enough contact area, just clean them with fine sanding paper and a rag dipped in some methelates spirits. Test continuety with your multimeter and see if the bi-metal strip/contacts works as it should.
If however this is a more recent acquisition it may have a solid-state temperate control module using a temp sensor and an SCR as a switch.
More tricky to test but it could then Indicate a faulty/intermittent temp sensor.