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A 10k pot across the 12V supply will dissipate (12 squared)/10k= 14.4mW which is nothing.Sceadwian said:Make sure it's rated for the wattage it's going to be wasteing or it's going to get awful hot.
The fan draws 0.5A at 12V. If the pot is set to halfway then fan's current is about 0.25A.
The TIP31 transistor has a typical current gain of 160 so its base current is 0.25A/160= 1.6mA. The 1.6mA in the pot with 6V produces a dissipation of only 1.6mA x 6V= 9.6mW which is nothing.
If the transistor has current gain near its allowed minimum then the pot might get slightly warm.