I tried to use 'ert-remote-temporary-file-directory' in a test for an 
external package, but it ended up breaking some existing tests simply by 
requiring both tramp and ert-x. These tests indirectly used 'cd' (by way 
of 'compilation-start'), which triggered the failure.

Steps to reproduce:

   $ mkdir -p ~/src
   $ emacs -Q --batch -l tramp -l ert-x --eval '(cd "~/src/")'

Result:

   Error: error ("No such directory: ~/src/")
     mapbacktrace(#f(compiled-function (evald func args flags) 
#<bytecode 0xc43976fdbae86a5>))
     debug-early-backtrace()
     debug-early(error (error "No such directory: ~/src/"))
     error("No such directory: %s" "~/src/")
     cd("~/src")
     eval((cd "~/src") t)
     command-line-1(("-l" "tramp" "-l" "ert-x" "--eval" "(cd \"~/src/\")"))
     command-line()
     normal-top-level()
   No such directory: ~/src/

Looking at ert-x.el, I think this is because 
'ert-remote-temporary-file-directory' does some fixup on $HOME, but it 
was too aggressive. See attached.