A 6 inch deep chaffing dish pan will hold 7 gallons. That the biggest one I could find. I think any deeper and the chaffing warmer would be ineffective. It is quickest with meso cultures not as hot but it will maintain well. Going from cold to hot is slow by itself though.
For thermos I keep a teapot with hot water nearby to rush the temps some. Way to slow with the 6 inch pan by itself. TO much surface area open to the air. The 4 inch deep pan will hold 4.5 gallons and is fine by itself.