Penumbral microjets (PMJs) are short-lived, fine-structured, and bright jets that are generally observed in chromospheric imaging of the penumbra of sunspots. Here we investigate their potential transition region signature by combining observations with the Swedish 1-m Solar Telescope in the Ca II H and Ca II 8542 Å lines with ultraviolet imaging and spectroscopy obtained with the Interface Region Imaging Spectrograph (IRIS), which includes the C II 1334/1335 Å, Si IV 1394/1403 Å, and Mg II h & k 2803/2796 Å lines. We find a clear corresponding signal in the IRIS Mg II k, C II, and Si IV slit-jaw images, typically offset spatially from the Ca II signature in the direction along the jets: from base to top, the PMJs are predominantly visible in Ca II, Mg II k, and C II/Si IV, suggesting progressive heating to transition region temperatures along the jet extent. Hence, these results support the suggestion from earlier studies that PMJs may heat to transition region temperatures.