For the else block, it's simpler to iterate over the values() rather than the keys. (Mind the name of the variable...)

    else {
        for (values %$t_hash) { $total += $_ }
        # (use the statement modifier for if preferred)
    }
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The two blocks could also be combined into a single loop -- whether this is an improvement, I'm not sure. :)

sub sum_hash {
  my $href = shift;
  my $total = 0;
  for ( @_ ? @{$href}{@_} : values %$href ) {
    $total += $_;
  }
  return $total;
}
[download]

If @_ contains any elements, iterate over a hash slice using the contents of @_ as the keys; otherwise iterate over all the values in the hash.