The Mars Science Laboratory (MSL) was protected during its Mars atmospheric entry by an instrumented heatshield that used NASA's Phenolic Impregnated Carbon Ablator (PICA). PICA is a lightweight carbon fiber/polymeric resin material that offers excellent performances for protecting probes during planetary entry. The Mars Entry Descent and Landing Instrument (MEDLI) suite on MSL offers unique in-flight validation data for models of atmospheric entry and material response. MEDLI recorded, among others, time-resolved in-depth temperature data of PICA using thermocouple sensors assembled in the MEDLI Integrated Sensor Plugs (MISP). These measurements have been widely used in the literature as a validation benchmark for state-of-the-art ablation codes. The objective of this work is to perform an inverse estimate of the MSL heatshield material properties and aerothermal environment during Mars entry from the MISP flight data.