Yes. A thermostat that's stuck closed blocks coolant from reaching the radiator at all, which traps heat inside the engine and can cause the temperature gauge to climb quickly, often within just a few minutes of driving, even if every other part of the cooling system is working fine.
The thermostat's job is to stay closed while your engine warms up, so it reaches operating temperature faster, and then open once it's warm enough to let coolant flow through to the radiator for cooling. It's a simple part, but it's also one that fails in a way that has an outsized effect on your engine's temperature. When it fails, it gets stuck closed, so coolant circulates in a small loop around the engine and never reaches the radiator to release heat, and the engine keeps getting hotter with nowhere for that heat to go.
This kind of overheating tends to come on faster and more dramatically than overheating from a slow coolant leak, since the entire cooling system is essentially cut off from doing its job rather than gradually losing fluid. You might notice the temperature gauge climbing steadily and quickly rather than slowly creeping up over a longer drive, and the radiator itself may feel surprisingly cool to the touch near the top hose even while the engine is running hot, since coolant isn't reaching it.
A thermostat can also fail, stuck open, which causes a different problem: the engine takes longer than normal to warm up. It may run cooler than ideal, especially in Ann Arbor's colder months, which can affect fuel efficiency and heater performance without necessarily causing overheating.
Because a stuck thermostat looks similar to several other overheating causes from the driver's seat, it really does need a hands-on check to confirm. If your Jeep runs hot quickly after starting, or your heater takes unusually long to warm up, Hoover Street Auto Repair in Ann Arbor can test the thermostat directly and replace it if it's the cause.