Interesting secondary effect you're going to run into at these flow rates.
Mechanical only thermostatic valve (e.g. car thermostat) requires a minimum
flow to maintain equilibrium temperature with working fluid.
At very low flow rates, any heat lost out the valve housing will affect the
measured temperature.
Solvable, but an interesting heat transfer problem of it's own.


Your servo concept is interesting, might refine it as a pager motor direct
driving a small (#4-40? smaller?) screw and nut, let that push on a small
lever and pinch your existing tubing.
I don't see that meeting your price target, and your size target will be a
significant challenge.


Is there a reason you have to control flow rate to maintain temperature?
>From here it looks like managing the fluid's temperature with heaters or
peltier coolers may be an easier solution.
Doubt it meets the spirit of your power budget...


-Denny
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