The objective of this work is to formulate an analytical solution using generalized hypergeometric series to capture the thermo-mechanical response of a viscoelastic interface in contact with a rigid half-space across a nominally flat rough surface. The considered model seeks to investigate the rough surface's thermal creep as varied with the load applied and time. It is expected that the punch's rough surface behaves like a Maxwell viscoelastic material. Given that real surface roughness is demonstrated to possess fractal characteristics, a deterministic Cantor structure representation is used to approximate such roughness. When the punch deflects throughout the size range of the roughness, an asymptotic power low in this model is found that links both the punch's load and temperature to the asperity's creep. Arrhenius' equation is used for establishing the connection between temperature and creep tendency. In the case of linear thermo-viscoelastic deformation, the suggested model allows for an analytical solution. The model's output closely matches the experimental findings that are publicly accessible through the literature.