The diocotron spectrum for a simplified fluid model of Malmberg-Penning traps that includes compressional effects due to end curvature with finite temperature is investigated. A class of length profiles for which the linearized eigenvalue equation for perturbations can be integrated by quadratures (integrable cases) has been found. In such cases, there is only algebraic growth when the effective angular frequency has a maximum away from the axis (hollow profile), and the model is mathematically equivalent to the zero curvature (two-dimensional Euler) case. Furthermore, profiles that are slightly nonintegrable (the difference being characterized by a small parameter epsilon) have been studied, finding that the complex frequency of the unstable l=1 mode scales as epsilon(2/3). Analytical calculations (to be presented in a companion paper) and numerical simulations are found in agreement. For the density profile used, the growth rate of the unstable mode has a minimum at the plasma temperature of about 5 eV, which might be tested experimentally. (C) 2002 American Institute of Physics.