How should I reheat beef tenderloin?
Depends on the method by which you plan to reheat the meat.  The end result should be that the meat is slightly warmer than mouth temperature.

The most precise method is to heat a large pot of water to 90-100F/32-37C, and hold the temperature strictly in that range.  Put your meat in an air-tight bag and suck out the air.  Submerge the meat in the water and leave it there, stirring occasionally, until the meat reaches 90F/32C -- the more meat, the longer it stays (a steak would probably take about 20 minutes, while a big, solid hunk of the tenderloin may take an hour).  Of course, you have to mind your water carefully, to keep it at the right temperature, so this method is a pain unless you have some specialized and expensive equipment.

If you are reheating your meat by oven or microwave, don't rely so much on the settings on the equipment as on the readings of a good thermometer taken from the center of your meat.  Still, you want gentle heat only, to avoid overcooking the outside while the inside comes up to temperature.

For me, however, I simply allow my leftover tenderloin to lose its refrigerator chill, then "heat" it by dipping each bite in very hot sauce or gravy.