Corrections

The voltage regulator has an internal thermal shutdown so if it gets too hot it will shut itself down. It has a maximum junction temperature of 150 degrees Celsius (302 degrees Fahrenheit). Stepper motors are known to run warm. The stepper motor in the parts list has a maximum temperature rise of 80 degrees Celsius or 176 degrees Fahrenheit. This is the maximum increase in motor temperature above ambient that will occur in open air, during continuous operation at maximum running current at low speeds. So 125 degrees Fahrenheit is certainly within the maximum temperature rise rating of the stepper motor. You should be able to run your clock continuously with no problems.