An instant-read probe is cheap and does two useful jobs away from a kitchen.
Checking food is actually hot through. The Food Standards Agency’s barbecue advice is that charred outside is not the same as cooked inside, and a probe is the only way to settle that without cutting everything open. It applies equally to reheating a dense pan of something over a burner, where the middle can be cold while the edges are steaming.
Checking a cool box is actually cold. This is the one people skip, and it is the more important of the two here. A cool box with a couple of ice packs is usually somewhere in the teens by mid-afternoon, which is not a fridge, it is inside the range where bacteria grow. Guessing produces confident wrong answers in both directions. See cooling and keeping cooked food.
For that second job a cheap dedicated cool box thermometer that lives in the box is better, because you will read it without deciding to. A probe is the versatile option if you are carrying one thing.