In this Letter, we study the heat dissipated at metal surfaces by the electromagnetic field scattered by isolated subwavelength apertures in metal screens. In contrast to the common belief that the intensity of waves created by local sources should decrease with the distance from the sources, we reveal that the dissipated heat at the surface remains constant over a broad spatial interval. This behavior that occurs for noble metals at near infrared wavelengths is observed with nonintrusive thermoreflectance measurements and is explained with an analytical model, which underlines the intricate role played by quasicylindrical waves in the phenomenon. Additionally, we show that, by monitoring the phase of the quasicylindrical waves, the total heat dissipated at the metal surface can be rendered substantially smaller than the heat dissipated by the launched plasmon. This interesting property offers an alternative to amplification for overcoming the loss issue in miniaturized plasmonic devices.