Short answer: You probably CAN'T send 1000 e-mails at the same time, because most ISP's have limits on their outgoing connections to avoid SPAM and such.
Long answer: If it were me, I would use Python and
smtplib, read all e-mails into a list, loop the list and send each e-mail with a PAUSE (for say 7 seconds) after each mail has been sent.
There might be other ways, but that's how I would do it from the command line.
If you have access to a GUI, I suggest Thunderbird in combination with
Mail Merge.
Best regards,
HMW