Just Me said:
You should try a faster internet connection first before replacing the computer. Even just trying from a different location to see if it is your connection or computer.
I agree. The very first thing you should be looking at is how fast your upload speed is. If it is low, then that could be the biggest problem.
Many computers get hot when using webcams, especially webcam software not native to the webcam itself, like ManyCam and such (HUGE processor hog, at least on the Mac version). Unless you can see your computer's internal temperature through a program like SMCFanControl (on Mac), you won't really know just how hot it is inside there. If it's getting over 80 degrees celsius, then you have an issue to deal with. If it isn't, then as long as you don't maintain a constant 70+ degrees celsius, you shouldn't be doing a lot of damage internally.
Even with my hard drive fan not working in my iMac, I rarely get over 70 celsius, even while video editing (which takes up a huge amount of processor power).
Look into your ISP's speeds for your plan. And if you are using Comcast, pretty much
NEVER believe the speed they say you could potentially get on a home connection (not sure about how it has been since they went Xfinity, but when I used to use them, their upload speed, even at off peak hours, was absolute dogshit).
For the best performance, with a HD stream, you're going to want 1 megabit/second upload speed, as a bare minimum. I have 5 Mb/s peak upload, and even on peak hours if I run a speedtest, I am always above 4.9 Mb/s on my FiOS connection, even from my NJ residence to testing servers in California.