OK, this may sound stupid but whats mkinitrd? I have re-built my kernel countless times, but I've never done that. I would do the following:
make modules install
cp arch/i386/boot/bzImage /boot/kernelname
cp System.map /boot
If mkinitrd is a stage in one of these then forgive me.
Either way, it sounds like you can't create a temporary directory. Make sure you're compiling in a directory you have full permissions to (eq your home directory). If that fails, you could compile it as root. This is generally considered to be a bad idea, but having said that, I compile everything as root, because I use /usr/src and I don't want other users to have permissions to write there. Do as I say, not as I do.