Can molten aluminium be used to reduce iron oxide (rust) into iron?
Short answer: Yes.

Take a look at the Ellingham Diagram.



The line for aluminium oxide is lower than the line for the all the iron oxides. This indicates greater stability of aluminium oxide, or in other words indicates aluminium's greater affinity for oxygen. Thus, based on thermodynamics alone one would expect aluminium to be able to reduce iron oxides.

Based on this figure, one would also expect this reaction to be spontaneous at all temperatures. 

Important caveat, the ignition temperature remains critical. Just as a piece of paper will not combust unprovoked, even though the reaction is spontaneous, the thermite reaction needs to reach its ignition temperature. 

Additionally, of interest to you would be this paper. Given below is a DSC curve from it



The endothermic peak ca. 660 corresponds to the melting of aluminium, while the exothermic peaks correspond to the thermite reaction.

The activation of the process is reported as 145 kJ/mol, and according to he authors in the study the product is controlled by the diffusion of $\ce{Al}$ in $\ce{FeAl2O4}$