Most (basically all) new processors can damage themselves within 10 seconds of a cold boot without TCP or a HS/f. With just a HS/F on, i won't guess more than a minute.
TIM (thermal interface material) is used to fill up the gaps between the heatsink and the cpu. Otherwise the heat won't dissipate from the cpu to the heatsink and the cpu will overheat.
Yeah, think about the picture above. If that was all air in the white space, and thinking about how hot a processor can get. All that air will be trapped in there and really cant leave. So now you have tiny oven pockets heating up and holding more heat and then pop! Good buy processor.
i lapped it in this very room, using sandpaper and an extremely flat piece of glass.
400-800-1500-2000-2500 grits. drops temps by 3-5C. generally doesn't turn air cooling into phase change though.
i'd link guides, but they're in different forums and that's against site policy.. but generally what you want to do is mark an "X" across your cpu with a sharpie marker. start lapping with the 400 grit. when the X is gone, mark another X and start with the next finest grit... and so on until its mirrored at 2500 grit. if you sand real lightly with the 2500 grit sandpaper it should come out to be a mirrored finish between 2700-3000 grit smoothness.
wet sanding is suggested, just don't throw it into your computer until its completely dry and cleaned and has a little bit of thermal compound on it.
you need it to transfer the heat from the cpu to the heatsink, the TIM acts as something to fill in the gaps between the heatsink and the cpu. the best TIM i've used is Arctic Silver Ceramique... that's what i use on my 4.68ghz E8400