Car overheats while driving, can take 5 to 10 minutes to start, quicker if in stop and go traffic. But won’t overheat when parked and idling.
Under those conditions, I’d start with a new radiator cap. If you are losing any coolant, even a small amount, you could have a blown head gasket.
To me that sounds like the cooling system isn’t holding pressure properly. Good idea above to try a new cooling system pressure cap. But that won’t work if there’s a leak elsewhere. Note that a cooling system leak doesn’t mean the problem is the head gasket. Could be the water pump or where a sensor screws into the cooling jacket that’s leaking. A small leak might not show up as coolant under the car. But a small leak will prevent the cooling system from maintaining its designed pressure. There’s a test called a “cooling system pressure test” that is often useful for diagnosing this problem. Suggest to have that done before attempting any parts replacement guesses.
If you want to try a diy’er approach you’ll need something like this
Note: If your car has experienced a severe overheating incident in the past, that makes it much more likely the problem is the head gasket.