1) You should disable the timer after the first WM_TIMER signal is caught if you want to show only one single dialog box. You can do this using KillTimer().
2) Windows wants to keep the GUI up-to-date. Whenever a region on the screen should be updated, it is invalidated using InvalidateRect or InvalidateRgn. Now, for every "invalid" screen part, WM_PAINT is called in order to make in "valid" again.
If you don't do it (or just parts of it), Windows will call WM_PAINT again ... and again. One way is to call ValidateRect. In many cases BeginPaint() and EndPaint() are used to do the job.
3) Maybe most important: you should not just return FALSE! Try DefWindowProc() for windows and DefDlgProc() for dialogs. They will also take care of WM_PAINT appropriately.