The pilot is on and it looks good. I turn the thermostat up but nothing more happens.
Despite the simplicity of a Millivolt system,troubleshooting them is often not as simple, if you go by the book using a Volt/Ohm meter to test the generator and gas valve. The Pilot Generators are less tricky as they all put out 750 mv or 3/4 of a volt out of the system, in the system is where each result will be specific according to what gas valve is used, not all gas valves have the same ohm's values, and many newer gas valves cannot be ohmed due to the design!
They will read open every one of them.
The way to make it simple and assure you never get any call backs
is to take a AA battery and attach a wire to each end of the battery,
Radio shack sells battery boxes with leads built in for several dollars.
Remove the 2 leads from the gas valve coming from the pilot generator and replace them with the AA battery leads If the gas valve operates normally via battery, it is a good gas valve, if not it is bad.
If you apply voltage to the gas valve and get zero amp draw,the gas valve is bad. Do not leave the battery in place and operate the unit in this manner unless you are able to be diligently watching it, never sleep or leave etc, it is strictly for emergency use or testing.
Old time units had no pilot safety, the pilot valve was manually operated just like a garden hose, if the wind blew it out it still kept coming, however as natural gas is lighter than air it will vent if it is allowed to via the flue, propane units must have 100% safety for the pilots operation as propane is heavier than air and will not vent, it settles in the lowest spot making propane more dangerous in that respect than natural gas is.
750 mv is 3/4 of 1 volt, not much power, the thermopile makes this power by having 2 dissimilar metals co joined in the end of the thermopiles that impinges the pilot flame.
A temperature differential must be maintained across the thermopiles end, if the entire end of the thermopile is hot the power will drop off or stop all together, thus extinguishing the pilot.
Many homeowners make the mistake of setting the thermopile too far into the flame, heating the entire end, not just the top 1/3 portion thinking this will bake it into submission, or force it to make power when in reality it does the opposite.