Using cotton swabs, clean off the old thermal paste off the die of the CPU and the heat sink.

Use the strongest isopropyl alcohol you can find.

You want to dip the cotton swabs into the alcohol and clean off the paste.

Keep doing this until the white cotton remains white. this indicates it is as clean as possible.

Dry the heat sink and die with another cotton swab. Make sure than none of the carbon fibers are left on the die or copper plating.