Here's another way:

my $time = POSIX::strftime "%Y%m%d",localtime;
sleep 86400;     # wait until tomorrow :-)
my $log = $time . ".log";
[download]

I can't take credit for this, it comes from dominus's wonderful Infrequently asked questions list.

Update
Well, at least I thought it was. I can't seem to find it on there anymore....