We're going to need a little more information. Make and model of your laptop and it's SKU(the sticker under your laptop)? How old is the laptop in question? If the laptop is old(by a few years) and you didn't replace the battery ever since the laptop was purchased, then you might need to replace the battery.
On another note, you might want to also see if the rest of your laptop is hot, i.e, if the power input area feel warm or hot to the touch. What OS are you working with?
Yes, I too have faced this issue a few times even after disabling the fast boot option. The laptop doesn't shutdown properly. I generally leave my speaker jack to the laptop. After shutting down the laptop, the HDD usage light continues to glow and there is some current passing through the audio jack making a noise through the speakers. I assume that the laptop has not shutdown and it continues to discharge until none is left. This issue has started only after installing Windows 10.
There are a lot of other issues with handling power. Another one such thing is the laptop doesn't respond if left inactive for long durations of time. The screen is turned off and nothing responds, I have to do a forced shutdown ( the system is still running for some reason) by holding down the power button. I had changed the power options to never go to sleep or hibernate when connected to charger, but this still continues to happen. Windows 10 is really testing my patience.