Can I easily add a thermostat to a whole-house fan?
If you just want a timer,  it's easy to buy a line-voltage timer switch that you can drop-in where the current fan's on/off switch resides.  

If you want a thermostat, as the comments said you can find a line-voltage thermostat. THen you just need to run the hot feed from the on/off switch to the hermostat and then on to the fan.

Another option would be to use any low-voltage thermostat in combination with a 120VAC relay, but then you've got more parts, and need a low-V supply for the thermostat, so I wouldn't choose this option :-)