Cadillac BLS everything cuts off at operating temperature

My V6 2.8 Cadillac BLS cuts out when up to temperature - whether idling or after driving about 8 miles. Everything goes off like turning the key - though the rev counter sits at the last reading. It had been showing an occasional "Stability Control" warning for a couple of weeks but drove absolutely fine. On cutting out it displays "Stability Control, Gearbox and Limited Power". A mechanic with limited software found a P0700 error code which, I'm told, is a general Transmission Control Module issue. The car drives beautifully for 8 miles - no gear change issues, no misfire or spluttering, nothing. Then it warms up and stops. To hit all systems at once it must surely be something like an engine control module ?? - though I'm no mechanic and can't find anyone to have a look at it either. I've read that crankshaft position sensors might cause similar issues, but it doesn't have any other relatable symptoms. Any advice would be much appreciated.