I have a Pioneer TV hooked up to a Pioneer Receiver via HDMI, and the receiver also has a cable box, Blu-Ray player, and Apple TV connected to it as well. If I add a Wii to the receiver, will it overheat any of the components?
No. The only reason things might overheat is if you have things physically stacked or unventilated (say by putting them in a cabinet without air holes.
Why would you think that a receiver would overheat if components are plugged into it? I assume the receiver has inputs for these different devices, so why would you think that it couldn't handle it? It's not like the receiver is processing input from all of the devices simultaneously and trying to output to multiple sources, etc. It's taking input from 1 place at a time, and sending it to one destination.
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As Alan said, you'd only have problems if there was a physical heat issue, exactly as he described (poor ventilation, or physically stacking components on top of each other)