Non-commutative theories show a remarkable mixing between ultraviolet and infrared degrees of freedom. In order to analyse some consequences of this phenomenon in a controllable setting, we study the one-loop dispersion relation for scalar excitations in supersymmetric, non-commutative theories at finite temperature. We find that in N=4 Yang-Mills the low momenta modes have superluminous group velocity for any temperature T>0. In the massless Wess-Zumino model the minimum of the dispersion relation is at non-zero momentum for high enough temperatures and we study the consequences on the phase structure of the theory. We briefly comment on N=2 Yang-Mills at finite density.