Keeping steaks hot after cooking in a cast-iron pan I have been using my cast-iron skillet for some time with good results.

Essentially, I bring out the meat from the fridge with time so it gets at room temperature, then I heat up my pan until it smokes and then I place the meat (with some salt and pepper and a little bit of oil) and cook it so it comes out medium-rare.

My issue is the temperature of the meat. As soon as I let it rest for 5 minutes after cooked, the meat cools down and it's no longer hot. I assume, since it has only been cooked for 3 minutes per side, that explains how fast it gets cold.

Is there any solution for this? How do restaurants do to keep the meat warm when it gets to your table?
If you cook rarer you don't need as long a rest period, for rare and medium-rare you only need a minute or two. Put the steak onto a row of chopsticks or a cooling grate if you aren't using a warmed plate so the plate doesn't cool them, then put a bit curved pot lid over the top. You can use a tent of foil if you need, it's just that there's less waste if you use a lid. 

If you are cooking many steaks and can't serve right away then put the cooked steak into an oven just a bit lower than the temperature you want at the center of the steak, this will keep it warm without overcooking it. Don't do it for too long though, you'll dry the steaks out.