Hi Legs, I don't know if our experience is of help to you but here you are.
We have two Dimplex heaters, several years old so not the oil free type you mention. One in a cold bathroom the other in a conservatory.
They do have a thermostat, three heat settings and a timer though this is mechanical not electronic.
These controls provide for great flexibility particularly how much of the day (and night) they are switched on. We find we only need to have them on for one quarter hour segment each hour at the lowest 1kw setting to provide basic warmth. When it gets cold in winter we up that to two quarter hour segments. We rarely need to use the 2kw setting, we've never needed to use the 3kw setting.
I would recommend them to you therefore though I'm not sure if the electronic timer will allow you to try the quarter hour technique.