In case the Anonymous Monk, or someone else with a similar homework ;-), needs the ** lines included, the feature that '..' in scalar mode returns an increment for every true evaluation and adds 'E0' on the last, can be used:

#!/usr/bin/perl
use strict;
use warnings;

while (<DATA>) {
    my $i = (/\*\*Temp/ .. /\*\*End/);
    print unless ($i && $i > 1 && substr($i, -2) ne 'E0');
}

__DATA__
first
second
**Temp**
fdvfd
fgd
dfgd
dfgd
**End Temp **
this is test
dffdgd
this is test
dffdgd
[download]

prints:

first
second
**Temp**
**End Temp **
this is test
dffdgd
this is test
dffdgd
[download]