After replacing iPhone 5s dock connector and Headphone kit, the phone gets too hot and drains battery

Sorry, but if you repaired the device yourself, then this is not the place to come for help. Find a DIY forum for iPhones to see if you can find help there.

Best of luck,

GB

The fact that you bought the flex on eBay says nothing about the quality of the part--eBay parts are notoriously the worst available, despite what the listing may claim. Nevertheless, heat = a short on the board. You can differentiate a board-level shirt from a bad part by booting the phone without the dock connected. Is it still hot? If so, then you can look for damaged/pushed components on the board near the dock connector under the sticker. This requires magnification and I would recommend that you take the phone to a professional for evaluation of this problem. The good news is that it is likely solvable.