Switch on a 10 A circuit with only a 20 mA signal
You could use a small pilot relay or a transistor to switch the automotive relay. 

An example of such as relay would be the G5Q-1A4 DC12  from Omron, about 1.50 USD each. It takes 16.7mA coil current. 

It's rated at 10A current so it may be able to switch the fan directly, but the automotive relay may last longer particularly if you don't put a diode across the fan. DC rating is 10A carry and 5A switched, so it's marginal and the initial surge may cause the contacts to weld so probably not a good idea. 

An RL44 is rated at 40A (resistive load) and the coil draws 140mA. 



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