DC motor. No load current variation with Temperature
The link in case 1 is pretty thorough - and includes the note that a true thermal model of a motor isn't that simple.
  There are three three losses in motors considered mechanical - iron losses (in the armature core), friction losses (bearings and brushes) and windage. These subtract from the electrical torque generated by the motor - to zero in the case of no load operation, obviously.
  Iron losses are fairy invariant with temperature, windage falls with temperature, but is probably negligible on a small motor - unless it has a shaft-mounted fan, and the bearing friction will also fall with temperature. Brushes are far from predictable, and their coefficient of friction can vary widely with temperature and surface condition of the commutator.
  Complicating all that is the temperature coefficient of the magnets. Most materials will reduce strength with temperature, and this affects the Kt value noticeably - so more current will be needed to generate the same loss torque. So will the no-load current rise or fall with temperature? That will all depend on the balance of the losses.