Some quick info about what temporary e-mail is, and what you should do about it as a service provider.
Temporary e-mails (temp mail) usually exhibit the following:
A temporary email address, or "temp mail", is based on the same idea as disposable email addresses. A unique email is given when asked for, but the difference is that with temporary emails there is no expectation for the user to ever read emails sent to that address.
They generate a unique temporary email when signing up for the service, and the email received is usually only stored for 10-15 minutes or up to an hour. After an email message has reached that age, it's irreversibly deleted. When using temporary emails, the user usually never ever has access to the email, or cares about it, after signing up, and maybe "confirming the email" by clicking a link.
The preferred way of doing user on-boarding is probably to only check if the e-mail is valid and allow the user to sign up. If they continue to use your service, then you can entice them to update it to a real address after a while, or when purchasing or changing settings.
Temp mails can be an issue if you are providing a monetary service, or if you have a cost for every new user. If you are running any form of contests, or vote counting, you probably don't want to allow temp emails, as they are really temporary, and a single user can generate millions of unique temp emails.
With our API you can easily check if an e-mail is a real e-mail, or a temp mail you should block.