analog circuit to convert one resistance to another
Yes it's silly to dedicate a whole arduino to running a fan.  But, step back and think what a arduino really is.  It's a little microcontroller with a lot of sugar coating around it.  You don't need all that stuff to make a fan run, so use a microcontroller directly.  There are many many small and cheap micros that are totally appropriate for dedicating to running a fan.  Most arduinos use Atmel micros inside, but there are also PICs from Microchip, MSP430s from TI, etc.

You really want to use PWM because it will waste less power, making less heat, requiring less means to get rid of the heat.  Even a few 100 Hz is good enough to run a fan.  There are plenty of small and cheap micros with PWM generators built in.  Once you set it up, you write the duty cycle value to a hardware register, and the rest is hardware that drives the fan proportional to that duty cycle value.