If I'm understanding the problem correctly, you need to open a file named "$Form{han}.txt" which contains a list of file names you wish to delete; you want to delete these files as well we the file "$Form{han}.txt". If this is what you need, then follow the example:

open (FNAMES, "<$Form{han}.txt") 
  or die "Cannot open $Form{han}.txt: $!\n";

while(<FNAMES>){ # for every line in the file.
  chomp; # remove trailing end of line character
  unlink $_ or die "Cannot unlink $_: $!\n";
}

close FNAMES; # close it before you unlink it.
unlink "$Form{han}.txt" 
  or die "Cannot unlink $Form{han}.txt: $!\n";
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Update: If you just need to delete the file "$Form{han}.txt" then all you need to do it follow mt2k's suggestion and:

unlink "$Form{han}.txt" 
  or die "Cannot unlink $Form{han}.txt: $!\n";
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1. Just a suggestion: Try using upper case file handle names rather than lower case ones.
   For example, try using 'THING' instead of 'thing'. This simply improves readability of your code.
   Using lower case is not invalid, just doesn't read as well as upper case :)

2. What is unlink <thing>; there? Never heard of removing a file by its handle...

3. The main reason is that you have the file open when you attempt to unlink it.
   The solution: close the file handle *before* you unlink it.

open(THING, "$Form{'han'}.txt");
#so far, you have nothing here
#code some stuff to deal with the file
close(THING);
unlink "$Form{'han'}.txt" or die "Couldn't delete $Form{'han'}.txt: $!
+";
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Cheers!

Update:
Ah, abstracts beat me to it and I see what he means.
You wish to read in filenames from the file and unlink those.
In that case, yes, do as abstracts says :) (or see below)

Update #2:
I couldn't let it go!
Here is another snippet that does the same thing as abstracts:

{
open NAMES, "$Form{han}.txt" or die "Oh my. File open failed: $!\n";
$/=undef;
for (split("\n", <NAMES>)) { unlink or die "Couldn't delete $_: $!\n";
+ }
close NAMES;

#Delete the file if you want to...
unlink "$Form{han}.txt" or die "Couldn't delete the data file: $!\n";
}
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Update 3:
Lol, still have one last thought on this idea.
If you only have ONE filename in the .txt file, then your code is almost right enough.
You'd just need to put the close() statement before the unlink one.
That would give you the following:

open(THING, "$Form{'han'}.txt");
unlink <THING>;
close(THING);
unlink "$Form{'han'}.txt" or die "Couldn't delete $Form{'han'}.txt: $!
+";
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