I know it could be many reasons since I’ve asked help from google...I think most probably is the overheating drains the battery.
I am not sure the generated heat was a result of a defective battery since my display did not set to higher levels or using the flashlight, games, heavy web and videos browsing. Sometimes these indeed suck my battery out of life very quickly. Anyway, I swap a MPJ 2500mAh battery which I bought with my Lumia 820 to troubleshoot if it was the problem of BP-5T, but it worked quite well. Also, the phone charger did not have any physical damage.
Then I tired to off the phone for one whole day and set display to even lower. After some steps indeed helped me discovered some apps that were pulling too much battery power cus after I installed these apps it stopped loosing its charge super fast. Luckily it was not a defective OEM battery but I already start in relying on quality replacement battery:)