Yes, the wiper contact can. But if you stay under the current spec, it should be able to handle it with minimal heating.
What I was referring to was that if you set the rheostat to some value in between the end points, you're only putting current through part of the resistance winding. The heat created is then only dissipated by the portion of the ceramic body where the current is running. (Assuming a two terminal connection to the rheostat.)
Unless specified otherwise, the power rating assumes the heat is dissipated over the whole winding and body. So in the example I gave above, if you dissipate 100W through 1/10 of the full winding, it's going to get a lot hotter in that 10% of the winding and possibly damage it.
That's all. I was just saying to take the current into account in rheostat applications as well as the power. The rating considerations are a little different than a fixed resistor.