An extension of the standard model , the Lee-Wick standard model , based on ideas of Lee and Wick was recently introduced . It does not contain quadratic divergences in the Higgs mass and hence solves the hierarchy puzzle . The Lee-Wick standard model contains new heavy Lee-Wick resonances at the TeV scale that decay to ordinary particles . In this paper we examine the behavior of Lee-Wick resonances at high temperature . We argue that they contribute negatively to the energy density \rho and pressure p and at temperatures much greater than their mass M their { \cal O } ( T ^ { 4 } ) contributions to \rho and p cancel against those of the ordinary ( light ) particles . The remaining { \cal O } ( M ^ { 2 } T ^ { 2 } ) contributions are positive and result in an equation of state that approaches w = 1 from below as T \rightarrow \infty .