First results on a diode-pumped multikilowatt-class ${\mathrm{Er}}^{3+}\text{:}\mathrm{YAG}$ solid-state heat-capacity laser (SSHCL) are reported. The laser achieves an output power of $4650\mathrm{W}$ and output energies in excess of $440\mathrm{J}$ . A moderate crystal temperature increase due to crystal heating of $56.7\mathrm{K}/\mathrm{s}$ is measured at $11.3\mathrm{kW}$ of pump power and the temperature-related power drop is determined to $8.8\mathrm{W}/\mathrm{K}$ . The presented work is believed to be the first multi-kilowatt-class resonantly diode-pumped ${\mathrm{Er}}^{3+}\text{:}\mathrm{YAG}$ laser.