Cooling of Jupiter's auroral thermosphere by H3+ radiation to space is one of the processes controlling the energy balance in the auroral upper atmosphere. The UltraViolet Spectrograph (UVS) and the Jupiter InfraRed Auroral Mapper (JIRAM) on board Juno have observed the Jovian polar aurora from its polar orbit since August 2016. The UVS instrument measures the H2 Lyman and Werner bands whose brightness is a proxy of the precipitated auroral electron flux. The 3.3–3.6 μm spectral window of the JIRAM L-band imager maps the H3+ thermal radiance with unprecedented spatial resolution. Comparison of concurrent observations indicates that the morphological features are similar in the two spectral regions but differences are also observed in the spatial intensity contrast. We compare the total (direct and indirect) particle heating rate and the cooling by H3+ radiation derived from four pairs of simultaneous UVS and JIRAM images. The total auroral cooling power H3+ is in the range 2–4 terawatts in both hemispheres. In all cases, the H3+ cooling in the aurora is found to range between 0.45 and 0.67 time less than the particle collisional heating. In a second step, we use the ultraviolet H2 brightness and FUV color ratio to derive the characteristics of the electron precipitation and model the H3+ radiance for each UVS map pixel. The comparison of the H3+ modeled radiance map with the JIRAM observations shows general good agreement with some local differences. The four spatially integrated H3+ cooling power from the model are in very good agreement with the JIRAM values. These results are important constraints for global magnetosphere-ionosphere-atmosphere models.