I noticed this when using password-store.el[1] which I use to look 
up
passwords using pass[2]

The file hasn't been updated since 2015 and I know it's been 
working so
I assume a recent change caused this.
Merely putting "x" instead of "" as the argument works fine.

[1] https://git.zx2c4.com/password-store/tree/contrib/emacs
[2] https://www.passwordstore.org/

Steps to reproduce

Starting from emacs -Q:
M-: (make-temp-file "")
;; Debugger entered--Lisp error: (file-error "Creating file with 
   prefix" "Permission denied" "/tmp")
;;   make-temp-file-internal("/tmp" nil "")
;;   make-temp-file("")
;;   eval((make-temp-file "") nil)
;;   eval-expression((make-temp-file "") nil nil 127)



In GNU Emacs 26.0.50 (build 1, x86_64-pc-linux-gnu, GTK+ Version 
3.22.18)
 of 2017-08-13 built on agro
Repository revision: a6ad98ad66e1d0c0dac5f25ba91e11d0cf9da725
Windowing system distributor 'The X.Org Foundation', version 
11.0.11903000
System Description:	Arch Linux

Recent messages:
For information about GNU Emacs and the GNU system, type C-h C-a.
Entering debugger...
Back to top level

Configured using:
 'configure --prefix=/usr --sysconfdir=/etc --libexecdir=/usr/lib
 --localstatedir=/var --mandir=/usr/share/man 
 --with-gameuser=:games
 --with-sound=alsa --with-xft --with-modules --with-x-toolkit=gtk3
 --without-gconf --without-gsettings --without-gpm 
 --without-m17n-flt
 --with-xwidgets --without-compress-install 'CFLAGS=-march=x86-64
 -mtune=generic -O2 -pipe -fstack-protector-strong -fno-plt'
 CPPFLAGS=-D_FORTIFY_SOURCE=2
 LDFLAGS=-Wl,-O1,--sort-common,--as-needed,-z,relro,-z,now'

Configured features:
XPM JPEG TIFF GIF PNG RSVG IMAGEMAGICK SOUND DBUS NOTIFY ACL 
GNUTLS
LIBXML2 FREETYPE LIBOTF XFT ZLIB TOOLKIT_SCROLL_BARS GTK3 X11 
MODULES
XWIDGETS LIBSYSTEMD

Important settings:
  value of $LC_COLLATE: C
  value of $LANG: en_US.UTF-8
  locale-coding-system: utf-8-unix

Major mode: Lisp Interaction

Minor modes in effect:
  tooltip-mode: t
  global-eldoc-mode: t
  eldoc-mode: t
  electric-indent-mode: t
  mouse-wheel-mode: t
  tool-bar-mode: t
  menu-bar-mode: t
  file-name-shadow-mode: t
  global-font-lock-mode: t
  font-lock-mode: t
  blink-cursor-mode: t
  auto-composition-mode: t
  auto-encryption-mode: t
  auto-compression-mode: t
  line-number-mode: t
  transient-mark-mode: t

Load-path shadows:
None found.

Features:
(shadow sort mail-extr emacsbug message subr-x puny seq dired
dired-loaddefs format-spec rfc822 mml mml-sec password-cache epa 
derived
epg epg-config gnus-util rmail rmail-loaddefs mm-decode mm-bodies
mm-encode mail-parse rfc2231 mailabbrev gmm-utils mailheader 
sendmail
rfc2047 rfc2045 ietf-drums mm-util mail-prsvr mail-utils help-mode
easymenu cl-print byte-opt gv bytecomp byte-compile cl-loaddefs 
cl-lib
cconv debug time-date mule-util tooltip eldoc electric uniquify
ediff-hook vc-hooks lisp-float-type mwheel term/x-win x-win
term/common-win x-dnd tool-bar dnd fontset image regexp-opt fringe
tabulated-list replace newcomment text-mode elisp-mode lisp-mode
prog-mode register page menu-bar rfn-eshadow isearch timer select
scroll-bar mouse jit-lock font-lock syntax facemenu font-core
term/tty-colors frame cl-generic cham georgian utf-8-lang 
misc-lang
vietnamese tibetan thai tai-viet lao korean japanese eucjp-ms 
cp51932
hebrew greek romanian slovak czech european ethiopic indian 
cyrillic
chinese composite charscript charprop case-table epa-hook 
jka-cmpr-hook
help simple abbrev obarray minibuffer cl-preloaded nadvice 
loaddefs
button faces cus-face macroexp files text-properties overlay sha1 
md5
base64 format env code-pages mule custom widget 
hashtable-print-readable
backquote dbusbind inotify dynamic-setting font-render-setting
xwidget-internal move-toolbar gtk x-toolkit x multi-tty
make-network-process emacs)

Memory information:
((conses 16 96356 5925)
 (symbols 48 20459 1)
 (miscs 40 48 104)
 (strings 32 29164 1340)
 (string-bytes 1 770963)
 (vectors 16 14155)
 (vector-slots 8 491071 8271)
 (floats 8 51 65)
 (intervals 56 237 0)
 (buffers 992 12))

-- 
Best regards,
Benny
                                0x9EC76EA52B8F32A1
6315 887D 6E46 6967 7AC0  3E76 9EC7 6EA5 2B8F 32A1