The item shown in the link on post #16 might possibly be useful. Maybe.

I think I would be inclined to use the comparator rather than spend a 'Fiver' ( £5 ) on it!
.

 

Comparator circuits are a mature category and many versions are available. The LM339 family of quad comparators includes four independent devices and costs less than the LM311, and so I recommend it as a better choice.

 

Why do you need four?
In any case, a $1.00 for LM311 is not going to break the bank!

 

With multiple comparators a window comparator is possible, That was what I got from the original post, the requirement for a window comparator.

I have seen the LM311 listed for quite a bit more, although not recently. Some distributors charge a lot more.

 

For N.A. suppliers, my first go-to is Digikey .
Order on the door step next day air.
Most N.A. suppliers show the LM311 from US 50c to 75c

 

Just a question for anyone here

The OP, did imply at the very start they might not be 100 percent at designing or building circuits,
but it does seem they have a bit more knowledge than 0, as they know about resistance and values.

so just wondering , all this talk about window circuits, compartors,
all good,
but I wonder, and maybe the OP could come back ,
so they want to learn about circuits, drivers,may be mains interface, or do they want a plug in and go answer.

 

or do they want a plug in and go answer.

I was under the impression they were after reviewing the original post, which is why I didn't elaborate on a 555 design.

 

which is why I didn't elaborate on a 555 design.

Here's the sim of using your 555 idea as a window comparator.
One advantage over a comparator IC is that it can drive a small relay directly.

The relay turns on (green trace) for the thermistor above 20kΩ (blue trace) and off when it goes below 10kΩ.
Since the trigger values are determined by resistor ratios (basically a bridge), they are quite insensitive to the supply voltage.