How this usually goes is:
Agent's E-mail: Please send me a partial.
Writer's Email: (hot diggity!) Thank you, it's on its way!"
This bit you edit out:
Writer's E-mail: (the next day) I just mailed you my partial, thank you again!
It's nice, but not needed.
Writer's E-mail: (two days later) You have my partial by now. I've got the rest of the book ready to go. Just say the word.
Writer's E-mail: (Three days later) Why haven't you written me?
Writer's E-mail: (Four days later) Still not heard from you yet. Is something wrong?
Writer's E-mail: (Five days later) I'm flying to New York and will be dropping by your office on Monday. We can do lunch, my treat!
Writer's E-mail: (Six days later) You stood me up, you *$#+! I'm coming over to your house to boil a bunny!
Writer's E-mail: (Seven days later) Ha-ha, that was just a joke. Seriously, please buy my book because now I need bail money....
No, we're always looking for the next bestseller, but time used reading well-intentioned thank you e-mails takes away from partial-reading time. A few seconds here and there adds up to hours rather too quickly. I shouldn't be here now, but I'm on break and terribly addicted to my craft.
If you absolutely cannot resist sending a thank you, then put a "No reply needed" ending on the subject header. I just did this today in regard to a what-not I sent to another editor.
One less thing for an editor/agent to do means more time for her to focus on your work.
Good luck!
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