My Honeywell space heater, radiant, oil filled model HZ-709 thermostat hysteresis way too broad - set to 70° will cycle >85°+ to < 60°. Replace thermostat? Dave

 

I have no idea how tight the control may be able to be but I would imagine it will never be good just because of the placement of the element and the sensor position. The thermal inertia will be quite wide. Placing a thermistor in the middle of the bottom just above the element and running an electronic control may help but just another thermostat will probably not help unless you go electronic. Those mechanical thermostats are not precision devices at all. If you go the way of the electronic control, add it in series with the existing thermostat so the old one will act as a cutout if the electronics play up.
This could be an interesting project as the thermistor can be tried in different positions.

This is an Ebay one that may work.
Just make sure you get one of suitable voltage and current.

 

I have no idea how tight the control may be able to be but I would imagine it will never be good just because of the placement of the element and the sensor position. The thermal inertia will be quite wide. Placing a thermistor in the middle of the bottom just above the element and running an electronic control may help but just another thermostat will probably not help unless you go electronic. Those mechanical thermostats are not precision devices at all. If you go the way of the electronic control, add it in series with the existing thermostat so the old one will act as a cutout if the electronics play up.
This could be an interesting project as the thermistor can be tried in different positions.
View attachment 303846
This is an Ebay one that may work.
Just make sure you get one of suitable voltage and current.

Thanks Dedad, it's just that the spec (online) claims control to +/- 2° and the LED displays credible ambient temp but won't cut in/out until +/- 15-20°. Ciao, Dave