I think the fastest way is to take a bus from Yanqing to Changping. From Changping South Street or North Station, there are minibuses from Miyun to Changping or Huairou to Changping. It takes half an hour to reach Huairou. The area around Beijing is too far. It costs 15 yuan to take a taxi from Huairou to Hongluo Temple.
If you are not sure, you can ask me.