If you want to prevent overcooking beef, you can't reheat it gently enough. Tri-tips are a relatively tough cut of meat to start with, and you don't want to waste the effort expended in cooking them to tenderness just to toughen them during reheating. Make "slow and easy" a sort of mantra when reheating -- and use a non-aggressive heating method -- to restore tri-tips to their former hot and tender selves.
Sous vide -- sealing food in a plastic bag and heating it in water that can hold a precise temperature -- is by far the gentlest cooking method and, by extension, reheating method. Sous vide prevents food from heating past the temperature of the water, eliminating the prospect of overcooking.
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Sous vide is most effective on beef cuts such as tri-tips. If you cooked the tri-tips to medium-rare, simple seal the leftovers in a food-storage bag -- vacuum-sealed bags work best but sealable storage bags are just as capable -- and set it in hot water that maintains a temperature of 130 F. Sous vide machines were once exclusive to high-end restaurants due to their cost, but you can many home models at reasonable price points.
If you don't have a sous vide machine, follow these steps:
Place the tri-tips in a sealable food-storage bag. Squeeze out as much air as possible and seal the bag.
Set a wide stainless-steel saute pan on the stove and a stockpot on top of it. The saute pan helps diffuse the heat and gives you more control over the water temperature. Fill the stockpot at least half-full of water.
Set the heat on the stove to medium and allow the water temperature to reach 130 F, for medium-rare, or 140 F, for medium. If you have well-done tri-tips, let the water heat to 160 F. Use an instant-read thermometer to measure the water temp.
Set the package of tri-tips in the water. Let the tri-tips heat for 30 to 45 minutes, turning them over occasionally if they float.
The oven is second only to sous-vide for gentle heating. Heat the oven to warm and tightly wrap the tri-tips in aluminum foil. Set the tri-tips on a sheet pan lined and place on the middle rack. Heat the trip tips for 30 minutes and check for doneness. Continue heating in five-minute increments until they are heated through.
Stovetop reheating performs best if you have a cooking liquid, particularly a matching gravy, to reheat the tri-tips in.
Add 1/4 to 1/2 inch of gravy or stock to a pan. Heat the stock or gravy over medium heat until hot.
Add the tri-tips to the pan and cover it with a lid. Heat the tri-tips for 15 minutes and turn them over.
Heat the trip tips for 5 to 10 more minutes, depending on the desired internal temperature: 130 F for medium-rare, 140 F for medium and 160 F for well-done.
Only reheat tri-tips one time. Repeated reheating exposes meat to the temperature danger zone, encouraging bacterial growth.