It is easily experimentally demonstrated that a focussed image of the Sun can be used to start a fire. Furthermore, by thermodynamic considerations or the conservation of étendue, it can be shown that moonlight cannot be focussed such that a fire can be created. However, it is theoretically possible to magnify starlight enough to create a fire, as the surface temperature of a distant star is still above the ignition temperature of tinder.
According to this article, there was a paper published in 2002 that included a design for a telescope capable of this. Does anyone know what the paper was? I've tried searching on Google Scholar and have found nothing relevant so far. My back of the envelope calculations suggest that in order to magnify Betelguese such that it had the apparent diameter of the Sun would require a magnification of at least 36,000 times. Assuming we were then going to focus this image to a small disk using a microscope objective, this would suggest we need an aperture of the order of 100s of metres in diameter... I'd be interested to see if there's a trick around this.