Shut off 12 volts 5 amps

Are you thinking of something like a mechanical thermostat. You may have to look at switching and reset temps though as they normally switch at a higher temp and reset at a lower temp. So you would need to take that into consideration when choosing a NO or NC circuit.

 

A thermistor. Usually used in conjunction with a level detection circuit designed around the required switching temperature.

You can purchase digital-readout, adjustable temperature controllers all over eBay and t'internet for a few $ that also incorporate a switching relay to let you apply/disconnect power as you wish.

https://www.ebay.co.uk/itm/High-pre...hash=item239b91d3a9:m:mPkQPvgXXvQF0StGvtUrNdQ

you can set this one between -50C and +110C and switch 10A max.

Note - if you're talking 40 degrees F then you would have to suitably insulate the sensor to prevent ambient temperature 'interference' with the switching level.

 

The device you state is the correct one but it doesn't work 'on its own' - it requires controlling circuitry. You still haven't stated whether you are working at 40F or 40C (I suspect 40F). For the higher temperature you could get a thermal (bi-metallic) switch that is 'passive' i.e. needs no controlling circuitry.
I have a thermal switch that is referred to as a 'frost detector' that will switch contacts at temperatures ranging from -5C to +5C but I haven't seen a purely bi-metallic (i.e passive) switch that operates at 40F.

 

A PTC thermistor is a 'resistor' that changes value with temperature. It is usually only capable of carrying a few 10's of mA of current so is employed in a comparator circuit who's output is used to switch another device - relay, transistor, triac etc.... these devices then control the higher current.

For the sake of a few $ it's simply not worth building your own hence my recommendation. There are simpler control circuits but you'll have to calibrate them yourself.

As for Murrays..... hang on, I'll pop out and check the 5.3 million people that comprise the Scottish population.... back in a moment......