Do not assume the disposer or all of its connected fittings are approved for boiling liquids. Check the manufacturer's temperature guidance and use a suitable alternative disposal method when that limit is unclear.
What the observation tells you
The grinding chamber, flexible connectors and surrounding sink assembly do not necessarily share the same heat tolerance. Running the motor is not a way to make an unsuitable liquid safe for the appliance, and mixing in an unmeasured splash of cold water is not a reliable temperature check.
A useful next step
Let cooking liquid cool safely in an appropriate container where practical. Keep oil and fat out regardless of its temperature.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.