If you wanted to have the set of files all open at the same time, you could store the file handles in an array or hash:

my %fh;
for my $i ( 2, 3 ) {
    my $fname = sprintf( "T%dT.txt", $i );
    open( $fh{$fname}, "<", $fname ) or die "$fname: $!\n";
}

# you now have multiple file handles indexed by file name in %fh
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But I gather that you don't really need to do that. If all you need is to read in file in turn, it's better to just have one open at a time. BTW, your comment about the strangeness of reading files line by line leads me to think you might like the following approach better:

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
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