Running echo sys_get_temp_dir(); does give the default temp, which is /tmp
This should be enough as the actual ini setting is as far as I can tell optional, introduced in php 5.5.
I made a test install on my account on x15 and I was able to install modules without any problem, despite the value not being set for sys_temp_dir. I tried both by using the upload inside Joomla and by uploading and extracting into the joomla/tmp directory.
Can you try now, and if it still fails please paste (or screenshot) the exact error message?