Assuming you simply disabled the "Wake On" options in the network adapter settings, there should be no way this would harm your system.
As to the temperatures in your computer rising as time goes on,, it's quite common when users forget to maintain their computers.. Try removing the cover from the computer , then use a can of compressed air to blow out all the dust and junk from around the processor, the heatsink, the power supply, and all vents and fans.. While you're in there, check to make sure all fans are working.
Hope this helps.
I just found the solution for the(when I put my computer into sleep mode and it wakes itself up a few minutes later or sometimes longer)and fixed it, when this was going on before I fixed it is there any way that it could have harmed my computer by doing that? And another question, since the temperatures are staeting to go up and it get hotter around my computer is it normal for temps to start going up and graphics card and cpu? I am noticing that mine is.