If you're looking for something "quick and dirty"... then you could just start your thread in the thread pool, and "wait" for the right time.
// By the way, this code would be *INSIDE* of the background thread. That's what
// the sentence above says, but apparently we devs only read code :)
while (DateTime.Now.TimeOfDay < myDesiredStartTime)
{
Thread.Sleep(1000);
}