I have a log.py module, that is used in at least two other modules (server.py and device.py).
It has these globals:
Python logging is thread safe:
Is Python's logging module thread safe?
http://docs.python.org/2/library/logging.html#thread-safety
So you have no problem in the Python (library) code.
The routine that you call from multiple threads (WriteLog) does not write to any shared state. So you have no problem in your code.
So you are OK.