In a multithreaded program, you have one of two cases: if it's running on a uniprocessor (single core, single CPU), then switching between threads is handled like switching between processes (although it's not quite as much work since the threads operate in the same virtual memory space) - all registers of one thread are saved during the transition to another thread, so using registers for whatever purpose is fine. This is the job of the context switch routines that the OS uses, and the register set is considered part of a threads (or processes) context. If you have a multiprocessor system - either multiple CPUs or multiple cores on a single CPU - each processor has its own distinct set of registers, so again, using registers for storing things is fine. On top of that, of course, context switching on a particular CPU will save the registers of the old thread/process before switching to the new one, so everything is preserved.
That said, on some architectures and/or with some OSes, there might be specific exceptions to that, because certain registers are reserved by the ABI for specific uses by the OS or by the libraries that provide an interface to the OS, but your compiler(s) generally have that type of knowledge of your platform built in. You need to be aware of them, though, if you're doing inline assembly or certain other "low-level" things...