Temp gage goes to HOT in six blocks. New thermostat, then new temp coolant sensor, problem continued. Flushed radiator twice with plain water and w/ flush solution, bled system, problem continued. Took car into rapair facility. Repairman checked pressure w/ device said can detect no leaks, refused to replace water pump (pump was replaced in 2006). I can see no belt going to pump. Start-up is some times rough I think you can briefly hear signs of growling or slipping, then settles. Timing Belt seems to have play in it to me. Could loose timing belt affect water pump function?
Have it block and pressure tested-do the block first to pinpoint a combustion leaking into the cooling system or a gas analyzer to sniff for hydrocarbons at the radiator fill neck.
Pressure test: do not do a pressure test if there's leakage at the headgasket this might cause coolant into the cylinders and lock it up or bend a connecting rod if cranked thereafter. The headgasket should be repaired before doing the pressure test.
If the block and pressure test passes check the following: Thermostat, Clogged radiator, Fan clutch, Radiator electrical fan, collaspe hoses, water pump.