  The behavior of supersymmetric theories at finite temperatures differs from
that of other theories in certain aspects. Due to the different thermal
statistics of bosons and fermions, supersymmetry is explicitly broken for any
non-zero value of the temperature. We study N=1 supersymmetric Yang-Mills
theory on the lattice at finite temperatures. This model is the simplest
supersymmetric extension of the pure gauge sector of QCD, describing the
interactions between gluons and their fermionic superpartners, the gluinos. At
zero temperature the theory confines like QCD, and chiral symmetry is
spontaneously broken. At high temperatures, deconfinement and chiral symmetry
restoration are expected to take place, but it is not known whether these two
phase transitions coincide or not. First results on this topic, obtained in
numerical simulations on the lattice, will be presented and discussed.
