How can I test an application for thread safety?

I have a working C++ application, using the same variables and objects in different threads without thinking about the consequences. I want to improve the application to be thread-safe (using mutex, atomic, etc...) - how can I test that the things I want to implement actually work?

My point is, that my application is already working fine without this - but I'm pretty sure it's just working because a possible error has not happend yet, and not because I have done something to prevent an error.