Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)For a topologically transitive subshift of finite type defined by a symmetric transition matrix, we introduce a temperature-based problem related to the usual thermodynamic formalism. This problem is described by an operator acting on Holder continuous observables which is actually superlinear with respect to the max-plus algebra. We thus show that, for each fixed absolute temperature, such an operator admits a unique eigenfunction and a unique eigenvalue. We also study the convergence as the temperature goes to zero and we relate the limit objects to an ergodic version of Kantorovich transshipment problem.131PROCAD UNICAMP-UFRGS [162-2007]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)PRONEX Sistemas DinamicosINCT em MatematicaCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)PROCAD UNICAMP-UFRGS [162-2007]