Probably not any more likely than on Earth. Actually, Curiosity's (MSL) rover's wheels are made out of aluminum and they've been grinding through iron oxide rust that gives Martian regolith and the whole planet its color for quite a while now. And Spirit and Opportunity (MER) rovers also use several tools, among which even grinders, made out of aluminum. So why this isn't a problem?
For thermite welding, you require very fine powder mixture of metal oxide and a metal that will act as a reducing agent when both are heated to a sufficiently high temperature to initiate the exothermic chain reaction. Very fine, often nano-sized aluminum powders are used for that, as it's a very strong exothermic reducing agent. Actually, nano-aluminum powders are often also used in rocket propellant mixtures as catalysts, or even on their own. A solid aluminum construction, or a tool made out of it, won't do.
Even less likely as aluminum also slowly forms a thin oxidized layer naturally (there is a bit of oxygen in Martian atmosphere too), or is protected intentionally such to give it a bit more surface strength, reduce its triboelectric potential, paramagnetism, or simply to additionally shield it against wear and tear.
What happens with thermite powders when sufficient heat is applied is, simplifying, that it excites individual granules to a point where metal oxide and reducing metal exothermically exchange oxygen atoms. This results in enough heat for surrounding, tightly packed granules that absorb this produced heat to continue the reaction on their own, setting off an exothermic chain reaction of sorts. For thermites with aluminum powder, this is called an aluminothermic reaction.
So you require not only all the ingredients and the heat to set the reaction off, but also a rather large quantity of such fine powders, well mixed and packed tightly together, so the reaction can be sustained. So, unless you've set that up intentionally, I don't see it happening spontaneously on Mars any more likely than it would on Earth. And it doesn't.