Differential thermostats, to control a fan on the cheap?

I've sometimes used the old type of non-electronic "turn the knob" central heating wall stats, which have both a turn on when cold, and a turn on when hot, terminal.

I mostly use Drayton

I will see if I have one to hand to check

For cheapness, scrap ones, replaced with modern, are sometimes on ebay or in the skip when heating system is modernised.

Incidentally, the old ones are often rated at 15A, and modern ones at 3A. I used one for heated towel rail, and one for pipe heater in garage.
 
I thought you had some smart home kit? If you're monitoring room temperatures this is some simple rules and a smart socket
 
Ah, what does "differential" mean in this context?
 
(If) the outside temperature is lower than (this) inside temperature, (then) I want (that) fan to run. I tried it with a simple thermostat with sensor on outside, and set it so if outside greater than 20ºC it turned off, but some times inside reached 27ºC so really wanted the fan on, also tried measuring inside only, if inside greater than 25ºC then turn on fan, but outside was 27ºC so actually heating up the house.

So if house temperature is higher than outside temperature want the fan to run, other wise want fan to stop, not perfect, as not opening or closing window, but with some luck it will reduce the days when we close all windows and use the AC, and if we hear the fan stop, it will alert us to shut the windows.

The main problem is we get up and house is hot from day before, so windows open and fan on to cool the house, but then the sun comes up, and before we have realised the outside is hotter than inside and we are heating the house with the fan. At moment it is not hot enough to worry, but likely as summer arrives it will get hotter, and a fan is far cheaper to run than a heat pump.
 
The main problem is we get up and house is hot from day before, so windows open and fan on to cool the house, but then the sun comes up, and before we have realised the outside is hotter than inside and we are heating the house with the fan. At moment it is not hot enough to worry, but likely as summer arrives it will get hotter, and a fan is far cheaper to run than a heat pump.

Reads like a job for a Rpi, or similar - you are not going to achieve what you want with simple stats.
 
There is a thermostat module in Home Assistant. I used it over winter to control the heat pad [via a smart plug] under my kumquat. This is basically that.
 
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