We analyze the performance of graphene microstructures as thermal photon detectors and deduce the range of parameters that define a linear response. The saturation effects of a graphene thermal detector that operates beyond the linear range are described in detail for a single-photon detector (calorimeter). We compute the effect of operating beyond this linear range and find that sensitive detection occurs for such non-linear operation. We identify the optimum conditions and find that single-photon detection at terahertz frequencies should be feasible.