You can use the join command like this:
join -t, -1 3 -2 1 -o 1.1 1.2 1.3 1.4 2.3 <(sort -t, -k 3,3 file1) <(sort file2)
It first sorts the files (file1 is sorted by the 3rd field) and then joins them using the 3rd field of file1 and the 1st field of file2. It then outputs the fields you need.