Room‐temperature superconductivity has been a long‐standing goal in the scientific community. For computational predictions, thermodynamic stability plays a critical role. Here, a high‐throughput screening is performed to study high‐pressure ternary clathrate hydrides with hitherto unexplored compositions. Two thermodynamically stable room‐temperature superconductors in the Li─Na─H system, based on the type‐I and type‐II clathrate structure types, both exhibiting superconducting critical temperatures (Tc's) exceeding 300 K under high pressure are uncovered. Remarkably, the type‐II structure, Li2NaH17, exhibits the highest Tc of 357 K at 220 GPa among all the reported thermodynamically stable hydrides. Random structure searches show that type‐II clathrate structures can also be stabilized with hydrogen deficiencies which lower the Tc. Superconductivity is shown to be the result of a Van‐Hove‐like singularity which can be tuned by the hydrogen content.