Combustion chamber wall heat transfer is a major contributor to efficiency losses in diesel engines. In this context, thermal swing materials (adapting to the surrounding gas temperature) have been pinpointed as a promising mitigative solution. In this study, experiments are carried out in a high-pressure/high-temperature vessel to (a) characterise the wall heat transfer process ensuing from wall impingement of a combusting fuel spray, and (b) evaluate insulative improvements provided by a coating that promotes thermal swing. The baseline experimental condition resembles that of Spray A from the Engine Combustion Network, while additional variations are generated by modifying the ambient temperature as well as the injection pressure and duration. Wall heat transfer and wall temperature measurements are time-resolved and accompanied by concurrent high-speed imaging of natural luminosity. An investigation with an uncoated wall is carried out with several sensor locations around the stagnation point, elucidating sensor-to-sensor variability and setup symmetry. Surface heat flux follows three phases: (i) an initial peak, (ii) a slightly lower plateau dependent on the injection duration, and (iii) a slow decline. In addition to the uncoated reference case, the investigation involves a coating made of porous zirconia, an established thermal swing material. With a coated setup, the projection of surface quantities (heat flux and temperature) from the immersed measurement location requires additional numerical analysis of conjugate heat transfer. Starting from the traces measured beneath the coating, the surface quantities are obtained by solving a one-dimensional inverse heat transfer problem. The present measurements are complemented by CFD simulations supplemented with recent rough-wall models. The surface roughness of the coated specimen is indicated to have a significant impact on the wall heat flux, offsetting the expected benefit from the thermal swing material.