We evaluate the Casimir interaction between a sphere and a plane, at arbitrary temperature, accounting for imperfect reflection. This enables us to study the rich dependance of the Casimir effect on the geometry, and to estimate the error made by the proximity approximation (PFA) commonly used in this sphere-plane configuration, which is the one of the experiments. For this evaluation we apply the scattering method, based on the theory of optical networks, to the sphere-plane geometry. The temperature is taken care of through the Matsubara formula. We use planar waves to express the reflection on the plane, and spherical waves for the reflection on the sphere, which leads to a multipolar expansion. The indices (l,m) for the spherical waves are truncated to maximum value for the sake of numerical evaluation. We first study the zero temperature case. We use the numerical results to characterise the error made the various approximation methods, depending on the model used to describe the mirrors, and to reveal correlations between the effects of geometry and of finite conductivity. We then analyse the dependence of the Casimir effect on the temperature. For perfect mirrors, we observe correlations between the thermal geometrical effects, that can yield to a repulsive contribution of the thermal photons to the Casimir force. This feature can be associated to the appearance of negative values for the entropy. Finally, we evaluate the Casimir effect for metallic mirrors at ambient temperature. We observe strong correlations between the effects of geometry, temperature, and dissipation in the metals.
