How about:

while(<TMPFILE>)
{

  if (/myword/)
  {
    $_.=<TMPFILE>;
    print;
  }
}
[download]

Basically, if the current line matches read and append the next line and print. The while loop only reads one line at a time(unless you change $/), so the nextline will just not be in $_ in your code, you have to read it in when you match myword.

HTH