In this paper we examine order reduction of parabolic systems using modal truncation. The parabolic distributed system is first approximated using the Galerkin method. The system matrices have a special structure that allows us to find the approximate spectrum of the parabolic system. To do this we compute approximate inverses of tridiagonal, diagonally dominant symmetric matrices. This approximation leads to algorithms of order O(n), as opposed to traditional algorithms of order O(n3), where n is the order of the system. Finally, an example is presented to illustrate the proposed algorithm.