Vanny and Demag you gave me something to look at a bit closer.
The probe was a cellphone

older style Nokia, you know one of the ones that dont break so easily. The Temperature gauge is pretty accurate on it but I am guessing that putting it against the grill in the centre of the dash would give such a low reading.
As for the heater beig fully closed well that part it was not because the taps got a small amount of crud that stops the gat as I call it closing properly (another of those will do eventually). Not really worried about a heater when you go a Cool air con system
When you say it cuts out, how do you mean 'cuts out'? Does it simply warm up? Or does a light go out? Or have you an indicator that the compressor pump has switched out?
What light? Did not even realise the basic BX system had a light? The only indicator is the fact it no longer blows cold air seems to be a big indicator its cut out. After I switch it off for ten minutes (time guessing here) it works again. It simply does not like prolonged use! But to be honest I rarely use it for long periods or drives so it does not worry me to often unless one these horrid humid days.
Time to get an electrical tester out I guess or take advantage of a free aircon check ( my bet is that Free means a repair almost certain

)