You'll probably need more memory before you need extra threads.
STAR is only fast at the expense of using a lot of memory. If you cannot acquire enough memory, then perhaps you should look at different aligners (e.g. bowtie2).
How big is your genome? If you are working with a human genome, the author of STAR (alexdobin) says that you can get by with 16GB of RAM in sparse mode (at the expense of speed), but you would need more like 30GB using the defaults. (see http://seqanswers.com/forums/showthread.php?t=27470)
What is your genome size? Star needs a lot of memory to generate and sort the suffix array. 32GB is very little RAM for this purpose and I just guess that the process started swapping. There are some parameters described in the documentation to lower the RAM requirements, e.g.
-genomeChrBinNbits 12, see http://seqanswers.com/forums/showthread.php?t=27470