Gas temperature in thermally supercritical cores under different conditions. The figure shows the gas temperature for a "low" cosmic‐ray ionization rate of ﹩1.3\times 10^{-17}﹩ s⁻¹, a "standard" rate of ﹩3.0\times 10^{-17}﹩ s⁻¹, and a "high" rate of ﹩6.0\times 10^{-17}﹩ s⁻¹. Because cosmic rays heat the gas directly, their rate affects the gas temperature in the intermediate region where the cooling is not dominated by dust and the heating is not dominated by hot photoelectric electrons. The figure also shows the gas temperature if the dust opacity is 4 times the "standard" value. This increase in dust opacity lowers the gas temperature everywhere, in the center and midradii by lowering the dust temperature, and at outer radii by increasing the shielding against high‐energy photons that generate hot electrons. Parameters are listed in Table 1.