I think Stadia games can run off of slower devices like a Google Chromecast settop box, and Android smartphone/tablet, so I think running Stadia games on a PC computer will not make a computer run more hot, or use more electricity compared to running games which are physically installed on a PC.
One of the benefits of Google Stadia maybe that it may not use a lot of RAM, CPU and video card power, and hard drive read and write cycles, so your PC won't run as hot and use less electricity than running offline games.
One of the benefits of Google Stadia maybe that it may not use a lot of RAM, CPU and video card power, and hard drive read and write cycles, so your PC won't run as hot and use less electricity than running offline games.