iPhone went dead and won't turn on even after charging

Hello guys, I hope someone can clarify this matter to me!

So my iphone 5s golden 16Gb is 18 months old and worked perfectly until 2 months ago when it would go dead and won't turn on unless I heat its back with a hair dryer.

The first time it went dead, II kept it plugged for over 12 hours on charge with no response, then I found out in a forum that I should heat it with a hair dryer. i did it and it worked, after a minute of heat, apple logo finally appeared. I did this in 3 different occasions where the battery went completely drained and it worked!

However the battery went dead again yesterday and I heat its back 3 times. On the 3rd time, iphone finally turned but the battery level kept 1% and it didnt go up even charging, while setting up the alarm, the phone again went dead and nothing happened since then (it's been 18 hours without my phone). Do you guys think it's time to replace the battery? Just wanna make sure that it's the battery because I will replace it myself, don't have enough money to take it to repair.