First off, I'd like to give a little disclaimer, opening your tablet and/or doing mods is dangerous for the tablet and could potentially lead to either breaking something or destroying your tablet. You're forewarned and I'm not responsible for any damage you do to your own device.
The Nexus 9 gets quite hot. Especially when holding the tablet directly on the back, the NFC antenna area gets quite warm because the SOC Tegra K1 is right behind it on the motherboard. The idea is to 1. Create better cooling performance and 2. Create a barrier for the heat so the back of the tablet no longer gets that hot.
Remove the back cover of the tablet. It's super easy. Basically if you have a decent fingernail all you need is that. Just gently squeeze your fingernail between the back and the aluminum side and you should then feel and hear a little popping noise. This is the tabs all around the cover popping off. Once you do this, you should be able to remove the back of the cover without damaging anything.
Get access to the motherboard. You'll notice the top of the tablet has copper foil at the top. This is the "shielding" which we will utilize as the heatsink. Obviously its very little copper and doesn't possess alot of thermal capacity to hold alot of heat. All we're doing here is creating a barrier so that the copper can soak up some of the heat from the Tegra K1 chip.
You don't need to remove the motherboard but here's what we're trying to get at. Behind this tin cover is the chip.
Add foam or a thick (1-2mm) piece of double sided tape that allows for the area to be compressed. This will basically ensure that the tin shield and copper are pressed against the Tegra K1 chip. This basically is the alternate to screwing down the heatsink like we would on a PC or laptop.
Put the back back on the tablet. You'll notice that the foam really sticks out and doesn't allow the cover to fully reattach to the tablet. You'll have to make sure its not TOO thick or the back won't go back on properly. Remember, the NFC antenna prongs are close to this area so you can't make it too thick or else the tablet won't turn on.
You'll notice the back is raised a tad in that area but it also feels very firm because the foam is pressing against the motherboard where the chip is. This will make us sure that the foam is doing the job of pressing the tin and copper shield against the chip.
After that you're done. It's a simple mod and it should drop your tablet anywhere from 2-5C for a little period of time. Obviously the cooling isn't active cooling so after a certain amount of benchmarking or stress on the chip, it'll begin to warm like normal.
Good luck. Let me know what you guys think. I considered replacing the tin shield with copper but decided that'd be a bad idea.