Hello,
We had some temporary difficulties in the last 2 days due to the large volume of emails.
Now the API working 100% properly.

Seems it’s impossible to generate new e-mail with TempMail API (at least there are not such methods mentioned in official documentation for the API).

The workaround is to fetch home page of TempMail service (the page will contain new e-mail as long as you don’t supply any cookies during request), parse it and extract e-mail. Quick and dirty “hack” with curl:

curl https://temp-mail.org/en/ | grep '<input id="mail"'

Result:

<input id="mail" onclick="select(this);" data-original-title="Your temporary Email address" class="mail opentip" value="xubakuwe@yk20.com" data-placement="bottom" title="" type="text" readonly>

Then you can interact with new box via API (just don’t forget to specify not e-mail address but its MD5 hash).

Obviously, it’s not a perfect solution. Because HTML layout of the page can be changed without prior notice (and you have to bother with parsing anyway).