What are the limiting factors when flying a model UAV plane to high altitude?
The same rules apply as for "real" airplanes, and the topic has been covered well in previous questions. With model airplanes, scaling laws make the task easier, rsp. the possible maximum altitude higher. I would suggest to hang the plane below a balloon to get it up without draining batteries. NASA has done it before with a remotely controlled glider.

For the limiting factors please see this question.

Here is a question for the maximum altitude of propeller aircraft.

Here is another on the feasibility of geostationary drones.

Depending on the acceptable fragility of the design, a model aircraft should easily go down to a wing loading of 10 $kg/m^2$ and then be flyable at 36 km of altitude. At a true airspeed of 155 m/s it will fly at half the speed of sound and the Reynolds number on the wing with an assumed chord of 0.25 m will be below 20,000. You need to fly it with a lift coefficient of 1.1, which will be a challenge at the low Reynolds number, and the L/D will probably be less than 10, so your propulsion needs to be quite powerful to hold the altitude up there. I haven't done the numbers, but the propeller will be huge. With back-of-the-envelope calculations, my answer for the maximum altitude is 36 km.

Turbulence should be of no concern - all flow patterns up there are of extremely large scale.

The low temperature should also be tolerable if all systems are electric. It is not so cold up there: The standard atmosphere gives -34°C.