I cannot reproduce your problem. The code you posted simply does not work. I added some required lines:

#!/usr/bin/perl -T

use strict;
use warnings;
use File::Spec;
use File::Temp qw( tempdir );

my $pathdir = $ENV{HOME};
(-d $pathdir) and File::Spec->file_name_is_absolute($pathdir);
my $workdir = tempdir("temp.XXXXXX", DIR => "log");
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Running that with taint mode, i.e. perl -T perlmonks.pl, creates the following error:

$ perl -T perlmonks.pl
Error in tempdir() using log/temp.XXXXXX: Parent directory (log) does 
+not exist at perlmonks.pl line 10.
$
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After creating the missing directory, there are no more errors or warnings:

$ mkdir log
$ perl -T perlmonks.pl
$
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Please post a Short, Self-Contained, Correct Example.

Generally, taint errors indicate that you have used data from outside Perl (i.e. environment, command line parameters, file contents) without a formal validation. See Re: When not to use taint mode for what taint mode actually does. It is pretty simple, not much more than a flag on a value that is hard to remove, "infects" other values with most operations, and causes a crash when a flagged ("tainted") value passed to selected functions.

Alexander