ABSTRACT 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 high-resolution, multiband ALMA observations of the far-infrared (FIR) continuum, CO ladder, and the C ii line. Using a visibility-plane lens modelling code, we achieve a median source-plane resolution of ∼200 pc. We use photon-dominated region (PDR) models to infer the physical conditions – far-ultraviolet (FUV) field strength, density, and PDR surface temperature – of the star-forming gas on 200-pc scales, finding a FUV field strength of ∼103−104G0, gas density of ∼105 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.