Heatsink mod question

In my quest to overclock ever higher without spending any money, I have come up with an idea for modding my heatsink- basically increasing its size and adding more fins from a different heatsink. My question is how do I attach this new part to the old heatsink? It seems like metal glue would not conduct heat well, same with solder. What's the best strong adhesive that conducts heat? And no, I don't have the ability to weld them together

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