Why not rig it the other way: pump water past the CPU, then through your coffee grounds? It probably wouldn't be great for your CPU, because the temperature required to properly brew coffee is hotter than you really want for your CPU. But maybe get the water to 80C, and a secondary heater after that.
Many years ago we used a hot P4 to heat mulled wine. https://imgur.com/a/mulled-wine-pc-WW1pW It could get to 60°C which is a bit low for coffee but was great for mulled wine
Incredible - thank you for sharing this.