Answer to "overheating after screen replacement"If the phone have been out of use for a while, it can be as easy as Andoid or Sony upgrade that make the phone warm. I experienced this with a z3.
Answer to "Original screen adhesive, how to use?"I use heatgun, but carefully. I have a heatgun (HG) with small nossle. First clean the edges of frame with isoproponol, then put the adhessive sheet with the glue side down. Use the HG to warm carefully the corners and use a tip of a tweezers to press so the adhesive stick. You can see it when it stick to the fram, it become more transperent. Then do the rest of it. Then take of the plastic "cover", install the screen and do the same heating on the screen it self. On the sides, make surre you heat only the 1 mm edge. I use my fingers with a paper or something to press and swipe the heated area to make sure the screen is pressed down until adhesive is holding it. Heat plate can also be used. There are many othe similar questions in the forum descriving the same.