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In sufficiently hot ionized gas, electrons radiate when accelerated in ion Coulomb fields: thermal bremsstrahlung is the main continuum cooling process. In the optically thin nonrelativistic limit its emission rate scales approximately asFor hot metal-poor gas this is the principal high-temperature channel. Metal ions still give important metal-line cooling near $10^6\mathrm{K}$, and in enriched gas can remain important up to several million kelvin; one should not infer that crossing $10^6\mathrm{K}$ instantly eliminates all lines. At sufficiently high temperatures most ions are stripped and free-free emission dominates. Inverse Compton cooling can also matter for ionized, diffuse gas in a strong radiation field, especially the high-redshift Cosmic microwave background. The high-temperature asymptote is bremsstrahlung cooling, with metal-line and Compton qualifications where appropriate.