temp not steady

2002 trailblazer LT model with 140K miles..4.2 6cly...there are no codes, but my coolant temp is not steady, it is constantly moving between 210 and 220 back and forth on the guage...i have already changed the water pump and the coolant. Any other ideas? perhaps coolant sensor or themostat? thanks in advance..Bob

This could be caused by air in the system or a sticking t'stat, did it do it before the work was done, heater work ok, any other symptoms?

This could be caused by air in the system or a sticking t'stat, did it do it before the work was done, heater work ok, any other symptoms?

yes, the temp started moving about a month ago before anything was touched. i do get good heat and AC is also fine. There are no other symptoms...i checked the coolant fluid levels both in radiator and overflow and both are at proper levels. I am leaning towards changing both the thermostat and coolant sensor because i have been reading that it can be a bit difficult to get the alternator out to get access to both of these parts, so only want to do it once, and besides parts not too expensive. am i heaqding in the right direction ?

Try bleeding the system first, see what happens.