Temp mail and private browsing address different needs.
A temporary email service provides an address for receiving messages, usually with limits on availability or retention. Private browsing changes how a browser handles certain session information on your device.
Private browsing does not automatically provide a disposable address. Similarly, entering a temporary address does not put your browser into a private session.
Neither feature guarantees anonymity. Websites can still receive information you submit, and signing into an account identifies that account to the service.
Choose the tool according to the task. Temporary email concerns where messages arrive. Private browsing concerns aspects of local browsing-session handling.
If a temporary inbox relies on browser storage, private browsing may also affect whether you can return to that inbox after closing the session. Check the provider’s access instructions.