Pragmatically, you're more likely to blow a fuse than cause a fire, but yes you need to know which wire is which so that you can install a new thermostat correctly.
If you don't have a multimeter then start by getting one.
Identify the incoming live to the existing thermostat. This should be easy.
If the old thermostat still operates (albeit at the wrong temperature) then use the multimeter to determine which of the remaining two terminals is the switched live (i.e. the one that becomes live when the dial is turned up).
At the programmer end, find the three wires, and determine whether those two wires go. The live should come come from a programmer 'CH On' terminal, and the switched live to a motorised valve (if you have one) or to the boiler/pump connection (if you don't).
I would expect the third wire to be connected to a bunch of neutrals somewhere. The fact that the insulation might suggest otherwise is irrelevant - you need to know where it goes.
If the green-yellow wire goes to earth, then it's possible that your old roomstat is a two-wire one, but just as likely that someone's wired it up wrong.
BTW, if it does turn out that the green/yellow coated wire is a neutral, then I'd slide some blue sleeving over it (at both ends) to avoid future confusion, and if you don't do this then you're indirectly breaching the Building Regulations and thereby breaking the law.