I believe an experiment was carried out in Arizona in recent times where an identical rifle was fired off muliple times and then the muzzle temperature recorded. It seems the muzzle never reached a temperature which could cause damage if brought into contact with human skin.
On the blue forum someone suggested that the muzzle had been heated on the kitchen Aga.
You're probably thinking of 'Bamber - The New Evidence' program with firearms expert, Philip Boyce. The Anschutz 525 appeared to be a carbine version, ie. shorter than that used in the WHF case, so not representative anyway.
It's also been discussed here, with the rifle end being heated in the AGA combustion chamber via the fuel filler-hole in the left-hand hot-plate, or in the ash-pit through a door at the front. Heating it on a hot-plate or in one of the ovens on the right-hand side would have been too time-consuming to reach the required branding temperature, if at all, imo.
Having said that, the burns could have been caused by a red-hot ejected bullet shell ricocheting off the mantelpiece wall, then onto the nape of Nevill's neck, getting trapped under his pyjama top.
Or by something completely different.