The coolant temp sender connector should have a red/white wire, that wire runs to the cluster and temp gauge
Disconnect connector and use a jumper wire to GROUND that red/white wire to battery Negative
Turn on the key
temp gauge should go up to full HOT
This means that red/white wire and the gauge are OK
If the connector has a 2nd wire, black/white, thats the ground for the sender, put jumper wire between red/white and black/white wires
Turn on the key
Should see the same Full HOT on gauge, if not loose or bad ground wire
If there is only the red/white wire on the sender then the THREADS of the sender are the GROUND, so do not use tape on the lower part of the threads, the sender needs a good metal to metal ground to the engine
If wires and gauge test as OK, then new sender is bad, period
Thermostat can also be stuck open causing lower operating temp
Heater can still be warm but not HOT
Start cold engine and open the hood
Feel upper rad hose and heater hose
Both will be cold
Let engine idle for 2 or 3 minutes
Feel both hoses again
Heater hose should be getting warm, upper rad hose should still be COLD, if so thermostat is OK, if upper rad hose is also warming up like heater hose then thermostat is open and shouldn't be