We usually hold our burger patties after smoking in a beef au jus, either french beef dip or oxo beef stock, we then put them on the flat grill to melt the cheese , and toast the bun, they seem fine for up to 4 hrs. or more and the left overs, get ground and put into Tacos or Chili
The juice is filled to cover them in the pan that then goes into the steam tray, or chafing dish we hold them at around 170