The present invention provides a traveling speed reduction gear lubricating oil cooling device that enables optimal temperature control for lubricating oil delivered via a lubricating oil pump that can be started up with a relatively small motor without running the risk of damage to an oil cooler in a cold work environment even when a temperature sensor that detects the temperature of the lubricating oil is installed outside a wheel mounting sleeve. During a startup operation, provided that the detected temperature at a traveling motor is higher than the reference temperature, the lubricating oil pump is driven at a speed in a lower speed range relative to the normal operation speed range. In addition, during the startup operation, the rotation speed of the drive motor for the lubricating oil pump is increased in correspondence to a rise in the temperature detected by a lubricating oil temperature detection sensor.