small fixable position motor to drive universal stage, possible?
To begin with, requiring the motor to bear the load is sub-optimal. Instead, a mechanical reduction drive stage, such as lead-screws, a gearing mechanism, or similar, is typical. In these, the mounting bearings of the reduction mechanism bear the actual load, while the motor does what it is best at, provide movement.

If the load is perceived to be very high, a clutch mechanism is sometimes applied, to save the motors from bearing wear during overloads.

To meet the "as cool as possible" requirement one may want to exclude both conventional DC / BLDC and servo motors from consideration: Both require some power to hold position against a load. Instead, consider stepper motors. 

For high precision angular (not linear motion) stages such as for laboratory laser alignment, there are two common approaches:


Stepper motors with high angular reduction: The reduction ratio is inversely proportional to the precision achievable, i.e. a 1:5 reduction provides precision figures one fifth of the step size
Stepper motors translating to linear motion (e.g. lead screws): This is ideal for small angular range, raising one side of a stage and lowering the opposite one.


For very small size stages, extremely tiny (and extremely expensive) ceramic piezo motors are used, offering increased stability, acceleration and settling speed compared to traditional servo motor direct drives or stepper motors with gear drives.

The Physik Instrumente web site linked above has some excellent references on such products, and implementations for a variety of alignment (including XYZ) stages. PI's piezo motors have been used in the Mars Rover so much in the news recently.