Wire in parallel thermostat and timer to an air extractor
When it calls for fan, the thermostat is going to short the R wire to the fan-control wire. 

You are proposing a timer which also shorts the R wire to the fan-control wire. 

Assuming it's all this simple.  

For the timer, easy enough: use any common lamp timer which allows hourly on/off.    Plug a "wall wart" type transformer into that which makes 24VAC.    Then add a 24V relay in the right place that connects R to the fan-control wire.   This way everything is Code and the most vulnerable component - the timer - is easily replaced.  

The arm-waving magic inside the furnace is what concerns me.  If you want help with that, you'll need to be a lot more specific.