Does it matter if I replace the PCR tube (usually made of plastic) with another material like aluminum, glass, or something similar?
The key property would seem to be, at first glance, thermal conductivity. According to this table copper wins. But then, what about chemical reactivity? Maybe gold is a better choice. And that brings us to cost and disposability. These factors make the choice of a metal problematic. That leaves plastic and glass. Glass has better thermal conductivity, but clearly it has other drawbacks.
Next to the cost for aluminium or any other metal, a lot of metal ions have chemical functions that makes them not suitable to do chemical reactions in tubes of that material. Copper, for example, reacts with oxygen and can therefore affect the reaction.
The article that rg255 posted in a comment says clearly that glass tubes have advantages compared to plastic tubes:
Heat transfer into plastic capillaries was slowed by thicker walls, lower thermal conductivity, and a lower surface area—to-volume ratio than glass capillaries. Whereas the denaturation and annealing target temperatures were reached by samples in glass capillaries, samples in plastic capillaries fell short of these target temperatures by 6°–7°C.
Nevertheless glass might have a big disadvantage: it breaks much easier than plastic. When you handle the tubes in the lab and don't pay enough attention you might lose your samples, and if you want to freeze some tubes and they are pretty full the glass might break due to the bigger volume of the frozen probe.