Where is the 2008 her coolant temp censor - 2008 Chevrolet Hhr

It appears to be on backside of engine block. Two wire connector, wire colors, tan and yellow.
No 1 is electrical for that sensor. I realize the picture isn't the best.

when a temp gauge drops to cold ,it indicates a problem in the cooling system
temp gauge sender units need water to activate the resistance that makes the gauge read so a falling gauge indicates no water around the sender unit --- air lock in the system--faulty wire connection to the gauge sender unit
the ac unit is not connected to the temp gauge so there may be another separate problem there
the temp sensor is an entirely different unit to the temp gauge sender unit and the short term working would be from an altered coolant level from changing that sensor --air lock in system
the temp sensor connects to the ECM to activate the fans and monitor engine operating temp so as to keep the air/fuel mixture exact for the engine conditions
the temp sender unit just makes the temp gauge read
a faulty thermostat will either be stuck open and the engine temp will take a long time to rise or it will be stuck closed and that will cause an overheat very quickly

P0420 means that the catalytic converter is operating below efficiency threshold. Normally, you only get this code if both O2 sensors ARE OPERATING PROPERLY. If you change the O2 sensors and still get the same code, it's an indication your catalytic converter needs to be replaced. But before you replace it, ensure that everything else in the engine is operating properly, so that whatever may have damaged your current catalytic converter doesn't damage a new one.

Check Ur air intake valve or Ur MAP censore some times when u change an electrical components other censors fail because they have been in use for so long that they get wear and tear and when u install a new part that new part may b working to its full potential but Ur other components may not b working to their full potential maybe a lil cleaning may do the trick
Try disconnecting and connecting them on to catch a better connection

I bet you the sensor is working great...its your thermostat thats done for. Sensor I believe is on the engine block itself...but as a rule...they either work or they dont.

THE 4.9L ENGINES COOLANT TEMPERATURE SENSOR IS ON THE THERMOSTAT HOUSING. WHICH IS LOCATED BEHIND THE DISTRIBUTOR. THE 4.6L ENGINES COOLANT TEMPERATURE SENSOR IS LOCATED ON THE BACK SIDE ENGINE THE SIDE FACING TOWARD THE FIREWALL BELOW THE EGR VALVE.

get your temperature censor(s) replaced. this will cause the fan to not come on if it is not functioning properly. usually the temp censor is somewhere that it can have coolant running on it so it can read the temperature on your car. your car will have one for the gauge and another one to turn the fan on and send signals to your ECM i suggest you replace both.

if the fans are not broken, here is a way to check them--- disconnect fans at wiring connection, then run a wire from positive on fans to positive post on battery,then run other side to ground if nessesary. if the fans are ok they will turn on. if not the coolant temp sensor is bad. or a short in wiring.

test your coolant if it is in specs.(you can get coolant tester from local auto part store for a low price) if it is not drain the coolant and use proper 50/50 mix coolant.
water pump and coolant temp sensor you had change already . get new pressure cab and make sure you dont have any leak from coolant system and run the car and check coolant fan works when engine reach or past the normal operation temp. if it not working you have to fix the fan but it is runing and you still have over heat should be pressure cab.

Yes, there is another one. The one you replaced is the coolant level sensor. The ECT (ENGINE COOLANT TEMP) sensor is located near the thermostat housing. It has a 2 pin plug on it.