What kind of Relay Reacts to Ohms?
If you don't need a lot of precision in your circuit, you can build a simple voltage divider as follows







simulate this circuit &ndash; Schematic created using CircuitLab

If you calculate the values in such as way that the voltage at output reaches the relay threshhold voltage, then when R1 get low enough to signal high temperature, the relay driven off the output will switch on. I think most mechanical relays are not very precise with respect to on-volate, so I would consider a solid-state relay for this.  

As an example, lets say you want your fan to turn on above 50 degrees (1k sense resistence), and your relay operates at 5V. Given that for a voltage divider \$V_{out}\ = \dfrac{R_{2}}{R_{1}+R_{2}}\$, we just plug in all the values to get the unknown:

5V = \$\dfrac{1K}{1K + R_2}*12V\$

\$R_2\$ = 1.4K, so you use a 1.5k Ohm resistor. The current losses in this voltage divider are only 4.8mA, so it isn't like you are throwing away a lot of power as heat. On the other hand, your triggering resistance is 1K, so at 12V you can only supply 12mA of current to the relay. This will be insufficient for most mechanical relays, but should be OK for solid state relays (SSRs).