Unless the fan had a huge base then you would not have been able to warm up a small plate, they all need a minimum mass of metal to detect.
I can warm up a large tin of confit de canard on a medium ring and a large tin of flageolets on a small ring but not a small tin.
A cheap single ring one is very usefull in the workshop for softening waxes, warming paint etc.
My smallest pans have a diameter of 90mm at the top and 80mm at the base and work perfectly well on my Siemens 9 'ring' Pro model hob. The plate that I cut had dimensions of 90mm x 40mm and easily straddled the smallest 'ring' and fired up the fan.
I could not live like that, far too hot. It is 14°C in our massive kitchen (7x6x3.6m. ) and a perfect temperature with one wood burner. The rest of the house has open hearth wood fires and being the two of us, we only light up the library hearth in the evenings while we read and listen to music before bedtime.(no telly). The hot air central wood furnace goes on when it gets to -5°C outside and that takes the chill off the house to make it more comfortable. The bedroom windows are closed while the snow and wind is around otherwise they are open all year so that we can hear the wildlife. (Moles making mountains).
14 deg - too cold for me to be comfortable! 23 is more like it for me in the evenings and 21 during the day when I’m pottering. I grew up in a cold house with just a gas fire in the living room. Bloody awful in the winter.
I think that PE and oh need to do something about draughty windows.