I can only offer my experience, which isn’t to say either method is better than the other. Heat treating with a heat gun takes more hands-on time but gives you more control and less chance of damaging the blank, but also doesn’t do as deep of a treatment.
A bed of coals heats the whole bow all at once and really deeply. I do think it makes them hold more reflex and perform better, but it just dries them out sooo much. In my experience, when it goes well it goes really well, but it doesn’t take much to go too far and end up with firewood. It definitely seemed to exaggerate the chance of failure if the bow had anything more than slight character.
Went through a phase where I made a pile of fire tempered bows. Some really fast shooters were born in those days, but also lost a fair amount of premium wood tinkering with the technique. I’ve since switched back to less intense heat treatments with a heat gun, and less intense drying in a hot box if the blank needs to lose a little leftover moisture.
Edited for more detail.