Compared with graphene, black phosphorene has direct band gap and higher carrier mobility, and has higher stability compared with siliconene. These superior physical properties make it a great potential application value in the design of new quantum devices. By combining the unitary transformation with variational method, the ground-state energy formula of polaron and hole-phonon interaction system in monolayer black phosphorus on a polar substrate is deduced, and the band gap formula is obtained. The influence of temperature on the energy and band gap of polaron, hole and hole-phonon interaction system is investigated. Numerical calculation for black phosphorus on typical polar substrates shows that the energy and band gap of polaron (or hole-phonon system) increase with the increase of temperature or truncated wave vector, and decrease with the increase of phonon frequency, which indicates that the energy and band gap of polaron in black phosphene are directly related to the substrate material, and the influence of temperature on the properties of the substrate can’t be ignored.