The propagation of acoustic waves along a cylindrical wave guide is typically analyzed under the assumption of a uniform temperature distribution over the cross-section of the guiding structure. However, if there is a nonuniform temperature distribution around the boundary of the waveguide (as occurs in an automobile muffler, for example) then there will result an inhomogeneous sound speed as well as a density gradient. This considerably complicates the mathematical analysis of the spectral structure of the waveguide. If the applied temperature distribution is a small perturbation of a uniform state, then the cut-off frequencies and modal shapes may be analyzed by classical perturbation methods (J. Acoust. Soc. Am. 102(1), July 1997, 160-163). However, for arbitrary wall temperature distributions, recourse must be made to numerical techniques. In this talk, a physical model will be formulated which incorporates both an inhomogeneous sound speed and a density gradient. The associated mathematical model is then a generalized eigenproblem. This is then discretized via the Control Region Approximation (a finite difference procedure admitting arbitary waveguide cross-sections) yielding a generalized sparse matrix eigenproblem. Numerical computations using MATLAB will be presented which highlight the alterations in the modal structure of such "warm waveguides".