Prime Rib = Heat Lamp

Heat lamp will be just fine. Cook it to rare, and get a pot of Thyme Au Jus boiling so when you get an order you can dip it for whatever prolonged period of time to cook it to its desired temperature. 

Lamps are good but be careful putting one to close can cook the product. To prove this put one close on something and you will actually see any external juiceon the roast boil. That heat eventually will penetrate so adjust the lamps spaceing properly.  Alto Sham ovens also hold well.

If you are doing this for a carved dinner buffet with prime rib as the feature here is how I do it.. You will need three things.. 1) A calibrated meat thermometer.. 2) Your Heat Lamp... 3) A hotbox that sits around 140 - 160 degrees. and/or a convetion oven with the blower set on low and set on 180 degrees or you lowest temp on the oven some only go down to 200 degrees and close the door until the blower kicks on.. (DONT SHUT THE DOOR ALL THE WAY)...

For step 1 you need your thermometer so rub your rib down in all your secret seasonings... then roast it however you roast it.. I normally roast mine at around 225 with a thick herb crust after I de-membrane it.. it takes about 2 - 2 and a half hours depending on a 12 - 15 pound ribeye... sometimes longer depending on the temperauture and return air outside.. But I will give you a guide for a sufficient temperature for serving

If you want your Prime Rib to be Medium Rare you will want to cook it to 110 degrees in the middle and obviously 120 degrees on the sides.. This will allow for carryover.. When the roast is done allow it to sit out for 15 minutes before you throw it into your hotbox or oven with the door cracked and blower on low at lowest temp possible..

------If you want it medium then I would do 120 in middle 130 on sides

------medium well 135 in middle and 145 on sides..(Why the extra five degrees? because people get finnicky about this temperature and usually dont know what they want... so you want to make sure its med well throughout if they request it)

------well done 150 in the middle.... dont care about the sides honestly (This is a crime)

Step 2/Step 3) Heat lamps are the best way to keep meat hot for carving.. But as a general recommendation Turn the heat lamp on and wait till the geusts start at the buffet.. then go back to the kitchen and bring the meat out yourself in front of them to carve as the chef.. (It not only looks good but it also assures your pulling the meat out of your hotbox/oven and the last minute possible to keep it as warm as possible as well)

I serve my meat medium rare 100% of the time and I am rated the best prime rib around this area yet you will get people who ask for it more done. in this situation keep a pot of boiling au jus in the back or an extra oven on... First offer to cut them a peice off the end to see if its done to their liking and if it isn't always offer to to cook it up more for them which id give to a cook who is helping watch your buffet or a server to take to the back and dump in the au jus then bring it out to their table as soon as it is ready... It is only proper..

Just my advice dont know how it is in your area.. Hopefully that helps..

Just a slight hijack.

"Au jus" means " with jus". As in, "prime rib au jus".

"Au jus" cannot exist on it's own. That pot of hot beefy liquid you keep beside the roast is a "jus". When the prime rib is served with that liquid, it is prime rib Au jus. 

Sorry. It s a pet peeve of mine, and an issue that was drilled into me by my Chef when I was but a green apprentice.

If its for a carving station, and/or you don't have access to an alto sham, then a heat lamp is the way to go. If you have access to an alto sham that would be my preference. Hot boxes will do too, just tough to contol exact temperature with one, especially if you need to keep opening and closing it ,