Submesoscale fronts, with typical length scales from 100s m - 10s km, are ubiquitous in the ocean. Submesoscale temperature fronts drive strong upward heat transport at mid-latitudes in wintertime, being comparable in magnitude to air-sea net heat fluxes, and assuming an important role on the global heat budget. Here, we explore how warming over submesoscale salinity fronts can alter sea surface temperature variability and the vertical heat transport direction, influencing ocean heat uptake and air-sea heat fluxes. We investigate the Texas-Louisiana shelf during spring/summer, as this region experiences enhanced heating and intense river discharge from the Mississippi-Atchafalaya rivers. We use satellite, shipboard data and numerical simulations to show that salinity fronts exposed to sea surface heating develop warm submesoscale filaments due to strong heat convergence. The high SST anomalies observed at salinity fronts lead to enhanced latent heat fluxes and to downward submesoscale vertical heat transport, which increases subsurface heat content. Satellite SST maps and a global analysis of the co-occurrence of salinity fronts and net surface heating indicate that heat convergence at submesoscale fronts might occur in different regions across the globe. This submesoscale process can only be resolved in high-resolution observations and simulations. Thus, the absence of these fronts in coarse resolution models can contribute to global model biases in SST and ocean heat uptake.