After 30 miles the temp gauge goes up to H?

Hello,

Having low coolant can surely make the engine run hot or overheat.
So, what happened after you added coolant? Did it overheat again or lose coolant?

It is possible that there was air trapped in the cooling system and it appeared to be full initially but as you are driving the correct coolant level showed up.

If you do not have any leak and the coolant level stays where it should with no overheating, it was simply low on coolant due to possible air trapped in the system.

You can try to purge the system again. One way to do it is, with the engine cool, remove the overflow cap. Start the engine, then squeeze the radiator hoses (be careful of any moving components) several times. This will let out any air that could be trapped. If the coolant level stays constant and no bubbles out of the coolant, then it is likely that air is out of the system.

If the engine still overheats with the coolant being full, it could be due to a stuck closed thermostat among other things like the radiator or the water pump.

https://www.2carpros.com/articles/symptoms-of-an-overheating-engine

Please let me know if you have any questions.
Thank you.