What should be done if an aircraft's engine shows signs of overheating during taxiing?

When an aircraft's engine shows signs of overheating during taxiing, the most prudent course of action is to shut down the engine immediately. This action helps prevent potential damage to the engine, which can occur if the overheating persists. Overheating can lead to engine failure or other catastrophic issues, and addressing the problem swiftly minimizes risks.

Shutting down the engine allows for a safer assessment of the situation by maintenance personnel. It also ensures the safety of the crew and passengers, as well as those on the airport ground. Contingent actions like continuing to taxi could exacerbate the problem further, and simply checking oil pressure or attempting to cool the engine by increasing throttle are not adequate responses to overheating signs and could lead to more severe consequences.