No, probably not water pump.
Could be the thermostat starting to fail or the heater core/by-pass getting clogged up, or fan clutch.
If the temp changes with RPM and speed then could be the fan clutch is bad.
After engine and radiator is warmed up shut it off and spin the fan blade by hand, it should move but not spin, i.e. if you try to spin it, it should stop as soon as you let go of the blade
I can't speak about every year but my '94 uses the heater core as the by-pass for the cooling system, there are no valves on the heater hoses, the heater core has coolant flowing thru it any time the engine is running, the heat in the cab is control by a door not a flow valve.
When the heater core got clogged up my engine temp would go up and down randomly after engine warmed up, uphill/downhill, idle or 2,500rpm didn't matter temp would go up just above 1/2 then drop back to "normal".
Changed a few parts before I got to the heater core on that one, lol.
On many vehicles they use a by-pass valve, it will have 4 heater hoses connected, it will be located by the firewall, these can get clogged up as well causing the same symptom.
Thermostats are suppose to fail OPEN(if they fail) so engine doesn't over heat, but they can fail closed or even open/close intermittently.
This is a less likely issue but not unheard of.
Water pump impellers(fins) can get worn down by cavitation and electrolysis, both caused by not changing coolant every few years, this can cause fluctuating temps, both only with RPM and engine load
Last edited by RonD; 07-03-2014 at 09:15 AM.