This work presents an experimental study on the mechanical behaviour of thermoplastic polyarlyetherketone (PAEK) based composite laminates reinforced with woven carbon fibres, subjected to high strain-rates under compression load. The specimens were tested using a Split Hopkinson Pressure Bar (SHPB) covering the working temperature and stress envelopes, -54°C, RT, and 80°C and 6 off-axis angles, respectively. The high-speed imaging system was used to monitor the failure process during the tests and the strain on the loading direction was determined using Digital Image Correlation (DIC). Fractography analysis was performed to identify and understand the influence of the temperature on the damage aspects, by the use of Scanning Electron Microscope (SEM). The -54°C and RT SHPB tests were found to have more intralaminar damage aspects than the ones tested at 80°C, which presented interlaminar damage aspect preference and the lowest strength. A new strain rate and temperature dependent failure criterion for thermoplastic composites was proposed based on a phenomenological approach and experimental results, where the fabric architecture at ply level is idealised as a two-part mosaic model. The crystallinity of the PAEK thermoplastic matrix was analysed using Differential Scanning Calorimetry (DSC). The DSC results showed no evidence of crystallinity degree variation due to the high strain-rate tests.