Thank you for sending this email.
You'd not typically use such a sentence (with either this or that) as part of a reply to the mail in question. There would have to be something special about the timing or content of the mail itself.
An appropriate usage would be if someone sent a message out to a number of people, including you. Then if you replied personally to them, you could quote the message and say something like:
Thank you for sending this email. I'd been wanting to
say the same, but I felt it would be overstepping my
authority to do so.
Using "This" instead of "That"
With quoting in context of a current conversation, you can use either "this email" or "that email" (all mails can be thought of as being in the past, unless the mail is describing itself). If you aren't quoting it or are discussing something from the past, you'd prefer "that email".
In either case, the wording will stress something unusually eloquent or timely about the email and the choice of when and how it was sent. So it's not something you would use casually to mean "Thank you for sending an email."
Here are some more common ways of just saying "Thanks for writing":
- "Thanks for the update."
- "Thanks for the note."
- "Thanks for the mail."
- "Thanks for getting in touch."