Thanks, so for motors, current determines the torque?
No! It's the other way round. Torque determines how much current your machine draws.
So in the same motor, provide it with either 5V or 12V and it will draw the same amps?
If so, let's say the motors current is 1A, so at 5V it will consume 5W and turn at "slow" RPM, at 12V it will consume 12W and turn at "fast" RPM (the torque will stay the same) but it will also have to be able to handle the extra 7W of heat?
No! It will draw higher current if you supply higher voltage as windage losses, vibration losses etc. depend on speed. Consequently, they load the armature more and more as the speed increases.
In DC machines, the major causes of heat are Joule heating in armature coils, brush contact voltage drop, iron losses (hysteresis & eddy current loss in armature core) and in the case of field excited machines, field winding copper loss (not applicable to permanent magnet machines).
So if you want a small 48v motor with low torque and high speed, to power a fan blade, it needs to be very low current, otherwise it will generate a lot of unnecessary torque and heat?
Just as stated above no machine can generate unnecessary torque. It's up to the user to extract it (of course only till the current is within the safe operating region for the given ambient temperature)

For a given power, the product of torque and speed is constant. You can either have a lot of torque and low speed or vice versa.
The speed of any electrical machine depends inversely on the number of magnetic poles. i.e. more the poles; less the speed; more the TORQUE PROVIDING CAPACITY.