my %filedata;
for my $i ( 2 .. 3 ) {
    my $fname = sprintf( "T%dT.txt", $i );
    open( I, $fname ) or die "$fname: $!\n";
    local $/;  # temporarily sets input record separator to "undef"
    $filedata{$fname} = <I>;
    close I;
}

# you now have the full content of each file as a single string value,
# indexed by file name in %filedata