Cursitor Doom writes:

Question is, what is the correct name for this 'mystery component' and
what should it read resistance-wise when cold?

... and (I forgot first time around)... why have they put a couple of
turns in each of the leads?

As others noted, it is a thermal fuse.

The turns are there for pliers or other tool to absorb the heat while
soldering the thermal fuse to the PCB. It's quite easy to blow a low
temperature rating thermal fuse while soldering.

What't the schematic like, are the resistors connected in such a way
that they would heat during some failure condition and blow the fuse ?

--
mikko