If you do not need access to the thread while it is doing it's job, you can free the handle you get from CreateThread right away with CloseHandle.
If you do need access to it, it probably means you are going to be waiting for some kind of result from it, which you can do using the WaitForSingleObject/WaitForMultipleObjects functions.
By the way, it appears there is a potential problem in your code; if the user presses Button1 a thread is created and the handle is stored in a global variable, if the user presses Button2 while the thread is running, this global variable is overwritten with the handle of the second thread.