Hi,
Could anyone suggest a cheap and easy way to control the air intake of a wood burning furnace using a servo? I would like to take a milliamp signal from a temperature sensor and convert it to a servo signal to throttle open and close an air control on the furnace using a servo to achieve a constant burn temperature. If temperature goes above a preset level then the servo would start to close the air control and vice versa.
The fastest and cheapest way would be a small microcontroller with an A/D-C, but I don't know how easy you find that.
If 8 bits of A/D-C resolution, even a PIC10F220 (or PIC10F222) should suffice

If you need through hole components, you can get 10 bit A/D-C in eg. PIC12F675 or PIC12F683.
It could be made analog, but would require a larger circuit, much more work and a lot of experimenting and tuning and each change would be time consuming - compared to changing a line of code.
What you consider easy is not for me to say though, so you be the judge and decide whether you want to go with a small microcontroller based circuit or a larger analog circuit.
If you have the sensor installed already, what kind is it?
And what output does it give over the temperature range you need the stove to be within?