Photothermal radiometry with an infrared camera allows the contactless temperature measurement of multiple surface pixels simultaneously. A short light pulse heats the sample. The heat propagates through the sample by diffusion and the corresponding temperature evolution is measured at the surface of the sample by an infrared camera. The main drawback in radiometric imaging is the loss of the spatial resolution with increasing depth due to heat diffusion, which results in blurred images for deeper lying structures. We circumvent this information loss due to the diffusion process by using blind structured illumination, combined with a nonlinear joint-sparsity reconstruction algorithm. The structured illumination is realised by parallel laser lines from a vertical-cavity surface-emitting laser (VCSEL) array controlled by a random binary pattern generator. By using 150 different patterns of structured illumination and our iterative joint-sparsity algorithm, it was possible to resolve 1 mm thick lines at a distance down to 0.5 mm, which results in a resolution enhancement of approximately a factor of four compared to the resolution of 5.9 mm for homogeneous illuminated thermographic reconstruction.