Thanks to everyone who replied. I am now in Chiang Mai and everything went smoothly, according to plan.

At Heathrow they were able to connect my bookings and check luggage through to CNX.There was a slight hiccup because I had not put in my middle name when booking the domestic flight. Apparently that can cause problems.

Arriving at Suvarnabhumi you leave the gate and just look out for the large overhead signs for domestic transfer to Chiang Mai, Phuket, etc. After about 400m you get to the transfer immigration check. There was no queue, it took all of 2 minutes to go through and you get a sticker to identify you as having to clear customs at final destination. Immigration exits right by the shops and restaurants that are central between A and B domestic gates. I headed off to the Thai lounge.

I texted from the plane at 15:57 to say I'd landed and got to the domestic lounge at 16:24. Not bad!

Domestic security was before the B gates. At Heathrow duty-free they had asked if I would have a transfer and put my bottle of gin in a sealed tamper proof bag. Thai security did check it very carefully, reading the receipt, before letting it through.

At CNX when de-planing you have to follow the signs and go to a separate carousel in the International end of the airport, clearing customs there.