A:AnswerYes, You should be able to use this thermal paste, but before going through the process of re-pasting the heatsink for your Xbox have you tried blowing it out with an air duster?
Sometimes the heatsinks collect dust and get clogged. That can lead to overheating.
A:AnswerI used this to completely redo my thermal paste on both my PS4 and PS4 Pro, and have had amazing results. It is even thick enough (be prepared to work with REALLY thick paste) that I was able to replace a torn thermal pad in the system. All of this said, if you decide to redo your thermal paste on the system, I would recommend a FULL disassembling of the system, and a thorough cleaning/dusting of every surface (don't forget to blow out the power section like I did on my first go at this). A VERY soft, large head paintbrush did wonders for me, combined with plenty of compressed air and an appropriate electronics brush. Also, don't overdo the paste or you could accidentally insulate the CPU instead of letting it dissipate heat. Basically, don't use more than enough to properly cover the surface without causing excess to squeeze out from between it and the heatsink.
A couple final notes: 1) I am sorry if I am saying obvious stuff. I don't want to assume you know more than you might and my advice cause you more problems than help. 2) All of this is advice from a consumer and not a professional Sony technician, so while I may know what I am doing, do not take my word as gospel and forge ahead. PLEASE double check my advice, as again I don't want to be the cause of more trouble than I have helped, as even doing everything I said might not help you with your exact problem. The overheating of your particular system could be caused by another issue. 3) Be EXTREMELY careful and find a well documented guide on disassembly of the system. And I highly recommend taking your own photos as you go so that you know exactly where each piece and exactly which screw goes where. A single thing out of place could potentially cause a short and destroy your system. 4) If you aren't comfortable working with delicate electronics, or aren't sure if you can minimize static electricity in your workspace, please find someone that understands what they are doing and ask them for help. Again, I know that is obvious, but I would rather say this out of extra caution than hear an accident happened.
Well, I think that is everything. I hope you get your PS4 running well again, and that this fixes your overheating issue! Take care, be careful, and keep on gaming on! Peace!