Is it safe to fork from within a thread?

Let me explain: I have already been developing an application on Linux which forks and execs an external binary and waits for it to finish. Results are communicated by shm files that are unique to the fork + process. The entire code is encapsulated within a class.

Now I am considering threading the process in order to speed things up. Having many different instances of class functions fork and execute the binary concurrently (with different parameters) and communicate results with their own unique shm files.

Is this thread safe? If I fork within a thread, apart from being safe, is there something I have to watch for? Any advice or help is much appreciated!