No, it is not recommended to touch the handle of a mug when it is inside a microwave oven, especially if the oven is operating and generating heat. The handle can become hot during the cooking process, potentially causing burns or injury if touched without proper protection.
When microwaving food or beverages, it's advisable to use microwave-safe containers that are designed to withstand the heat generated by the microwave. These containers are typically made of materials such as glass, ceramic, or microwave-safe plastics. They are designed to heat up while the food or beverage inside them absorbs the microwave energy, but they should remain cool to the touch.
If you need to handle a mug or container that has been microwaved, it is best to use oven mitts, pot holders, or other appropriate protective equipment to avoid burns. These precautions help ensure your safety and minimize the risk of injury.