Can I use a wild card with unlink?

Indirectly, yes. unlink can take a list, so just supply it with the result of a glob (careful since unlink with no arguments unlinks $_):

my @files = <*.tmp>;
if (@files) {
 unlink @files or warn "Problem unlinking @files: $!";
} else {
 warn "No files to unlink!\n";
}

# Or
unlink or warn "Problem unlinking $_" for <*.tmp>;
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Update: I thought that unlink with an empty list would act the same as unlink with no arguments, but I was wrong, so boo_radley's answer is perfectly ok, except for the lack of error checking, if you care about such things :)