i was curious about this, because we have a burger stand close to where i work that isn't very big but they get a huge lunch crowd every day and the service doesn't slow down... the other night i went in and the owner happened to be there, so i asked him how they do it. the patties are 1/3lb no fillers, grilled to medium-well that morning before the rush, then placed in broth (knorr ultimate beef base, 4oz per gallon of water) and kept in the cooler, about 40 patties per sheet pan. they finish/reheat in about a minute on the grill.
it works well, i've been in there when it's been buisy or slow and i never noticed any difference in quality. they use good ingredients, that probably makes a big difference...