The AstroMesh antenna is an example of a mesh reflector with perimeter truss for use as a large aperture space antenna. A quarter model of such an antenna, with the original mesh supplemented with a continuous membrane, was analyzed in nonlinear finite element code ABAQUS. In particular, we investigated requirements for maintaining the initial parabolic shape under thermal perturbation. An RMS error was calculated for different thermal loadings as a measurement of deviation of the perturbed surface from a reference parabolic shape. Thermal contraction or expansion of the membrane boundary springs was found to offer reduced RMS error, but at the cost of higher spring reaction force. Electrostatic pressure was also applied to different membrane regions to acheive better RMS error with minimized spring reactions.