No idea about Windows. On a Mac it's simple.
• sudo du -ah / > ~/Desktop/fsdump.tmp
• install your app
• sudo du -ah / > ~/Desktop/fsdump2.tmp
• diff ~/Desktop/fsdump.tmp ~/Desktop/fsdump2.tmp
append
> ~/Desktop/diff_results.txt
to the last command if you want the results in a text file rather than printed to the shell.