Cooking dilemma; Update - Pic of cooked tenderloin on Page 2

Sear it over high heat on all sides, then move it over indirect heat for 30-45 for rare. If it was vacuum sealed, you could probably eat it raw so I would only worry about overcooking it.

Or just go to the store and get a cheap probe that you wouldn't mind throwing away before you leave. Shouldn't be more than like $5 at a grocery store.

Cut into individual steaks.

Pan sear

Profit

How Do I Cook Steak?
First start out by letting the steaks rest at room temperature for 30 minutes (this brings them a little closer to room temp to cook more evenly).
Heat vegetable oil in a 12-inch cast iron skillet over medium-high heat (you want to let it get hot, preheating should take about 3 minutes if using a gas stove then more for electric.). I like to turn on vent fan above stove.
Dab both sides of steak dry with paper towels then season both sides with salt and pepper (some people might recommend to wait until the end on the pepper because it can burn but I’ve never tasted burnt pepper).
Place steaks in skillet and using metal tongs press down across top surface of steaks to ensure the entire bottom surface is making direct contact with skillet.
Let cook until browned on bottom, about 3 minutes.
Flip and continue to cook until steak is about 10 degrees away from desired doneness (see notes below for temps) approximately 3 minutes longer.
Reduce heat to medium-low, add butter, garlic and thyme. Using an oven mitt grasp pan and tilt pan so butter pools to one side, spoon butter over steaks and continue to cook until steaks registers temperature of desired doneness, about 1 minute longer.
Transfer to a plates, let rest 5 minutes before slicing.

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how do I cook this thing to rare without a grill and temp probe?

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You could just go to CVS or Walgreens and get a George Foreman grill for about 10 bucks.

New idea. Somewhat less smoke. Season and wrap in foil and cook in the oven at about 275F for about 45 minutes, then sear it off in the skillet on all sides. That should be enough time for a 2lb cut to be just below or at rare. As the others said, really need a temperature probe to do anything other than guess. I would err of the side of undercooked. That's easy to fix.

There are a lot of really good restaurants in DC.

You’re going to set off the fire alarm at the hotel if you want to cook this thing properly.

Find a park with grills