We present a sub-kpc resolved study of the interstellar medium properties in SDP.81, a z = 3.042 strongly gravitationally lensed dusty star-forming galaxy, based on highresolution, multi-band ALMA observations of the FIR continuum, CO ladder and the [C ii] line. Using a visibility-plane lens modelling code, we achieve a median sourceplane resolution of ∼200 pc. We use photon-dominated region (PDR) models to infer the physical conditions -far-UV field strength, density, and PDR surface temperature -of the star-forming gas on 200-pc scales, finding a FUV field strength of ∼ 10 3 − 10 4 G 0 , gas density of ∼ 10 5 cm −3 and cloud surface temperatures up to 1500 K, similar to those in the Orion Trapezium region. The [C ii] emission is significantly more extended than that FIR continuum: ∼50 per cent of [C ii] emission arises outside the FIR-bright region. The resolved [C ii]/FIR ratio varies by almost 2 dex across the source, down to ∼ 2×10 −4 in the star-forming clumps. The observed [C ii]/FIR deficit trend is consistent with thermal saturation of the C + fine-structure level occupancy at high gas temperatures. We make the source-plane reconstructions of all emission lines and continuum data publicly available 0 .