In the beginning, there was mktemp. And it was good.
Actually, that's a load of rubbish, it wasn't good at all. By separating the "give me the name of a temporary file" and "open the file" stages, there's a chance for an attacker to create the temporary file with the name you've chosen between the stages, or create a symlink with the same name.
Next there came mkstemp. And that was better. But not by much. mkstemp opens the file for you as well as choosing a name, so the file was guaranteed to not exist beofre you tried to use it, and will definitely have the ownership and permissions you want.
There is yet another step which the über-paranoid application could take in order to ensure that no other process can see its temporary files, and that is to unlink the file as soon as you get it back. Unfortunately there's no "mkstempr" function (and it might get confused with the equally non-existent mkstemp_r), so this is still a two-stage operation. Unlinking a file which you have open removes it from the directory listing, but doesn't change the fact that you have it open; it's now exclusively yours.