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.