Processors generate alot of heat since they are very small chips, but do alot of processing and alot of current goes through.
Without thermal paste or a heatsink, think of your processor as a melted block of plastic, because thats all it would be, even after about 5 seconds of not having one on it, since it'd get to about 300 degrees or something mad like that and just melt.
The thermal paste goes onto the processor and is bascally heat conductor which helps the hot air rise from the processor, to the heatsink which goes ontop of it.
What the heatsink does is again, transfers the heat (usually Copper) up using a special technique, and then this then rises to the fan, and the hot air gets blown out.
All this in turn keeps the processor running at a good temperature (around 45 degrees C) which is alot better than it melting
Why do you want an AGP card and motherboard? If you go for PCI-E, you'll get more out of your PC when new graphics cards come out because its a newer technology.
I hope this helps
(Sorry by the way draconum, I didn't realise you'd already posted a reply. I was still writing this when you posted)