Is there an exact process to determine the "as it should" requirement? Mine seems to hit three bars more often than it did, and I'd like to be certain the fan is operating "as it should"...As the engine heats the pressure in the system forces excess coolant into the reservoir tank. If the tank fills it overflows overboard. As the engine cools and pressure reduces, coolant is pulled back from the reservoir. If more fluid is needed than is in the reservoir air is pulled in.
As the coolant heats to the boiling point it can easily fill the reservoir and cause it to overflow, and then when it starts to pull the coolant back in as it cools there is not enough volume to fill the cooling system. Sounds like this might be what happened to you.
It could be that you've got a lot of air in the system, and air doesn't provide any cooling. Let everything cool down, fill the system at the radiator, and purge the air from it. If there are no other cooling system problems (i.e. bad water pump or something plugged) you should be OK. Also check the radiator fins for damage and make sure the electric fan comes on as it should.