Why is processor running so hot during a video conversion?

The computer would have shut down if it were actually running that hot, so I would say that the temperatures are an illusion.

You can use RMClock, as it has a display that shows the state of "throttling". If the processor's temperature goes over about 70C, the processor reduces its processing rate for short periods to control the temperature, which you would see that in the RMClock graph.

So if you don't see throttling, then you know the real processor temperature is not 118C. What you want in a hardware setup is to not lose any performance. So, if you see the graph dip when AGK runs, then you need more cooling, or to clean, apply paste, and reseat the processor's heatsink and fan cooler.

I have had trouble with a heatsink and had to put it on a few times to convince myself it was seated correctly. I look for a little paste to "wet" the joint between heatsink and processor. I mount the heatsink on to the motherboard outside the PC case, so I can be absolutely sure it is where it is supposed to be. I take the heatsink off the processor at least once to make sure the spreading pattern of the paste is right. My current heatsink is bolt-on unit, which allows me to control the clamping force. It fastens from the backside of the motherboard, which means I have to take my computer all apart to work on it.

The heating could be caused by a defect in the processor, but it's more likely to be some weird software problem. Using RMClock should set your mind at ease.

To verify temperatures with complete certainty, place a fast-response cooking thermometer against part of the heatsink not exposed to the fan air flow. Nothing fancy is required, just a £2/$3 dial thermometer.