Just a thought experiment I'm pondering regarding the idea of a computer case which conducts heat while insulating all of the sound inside.

There's multiple holes in the idea when fully formed regarding financially reasonable, allowing air-flow, etc, but to keep this question narrow I want to just dismiss all of those concerns for the thought experiment and ask what the question title is:

Are there any materials konwn to be sound-insulating but thermally-conductive?

I recognize conducting one type of energy while insulating against another is not a straight-forward thing, the closest that comes to mind is water, but that's not even accurate because it does conduct kinetic energy (i.e. hydraulics), but it acts as a sort of low-pass filter as well.

So if no materials come to mind, I'd be interested in hearing of something that could filter sound very effectively while conducting heat as well.

I'd like to put the qualifier that the material is a solid, but I'd be interested really in any material with these properties just because I believe (perhaps wrongly?) that there are likely a very small number of them. Again, don't think in terms of the goal concept I mentioned regarding a computer case, this is just one step towards that thought experiment (which is likely not reasonable, or else products would be on the market right now that provide such).

Are there any materials known to be sound-insulating as well as thermally-conductive?

Cost is not an overriding concern, but preferably costing "reasonable amounts" and much less than national defense spending levels.

This is a thought experiment that I'm pondering regarding the idea of a computer case which conducts heat while isolating or dampening all of the sound inside.

There's multiple holes in the idea when fully formed regarding financially reasonable, allowing air-flow, etc, but to keep this question narrow I want to just dismiss all of those concerns for the thought experiment.

I recognize conducting one type of energy while insulating against another is not a straight-forward thing. The closest material that comes to mind is water, but that's not completely accurate because it does conduct kinetic energy (i.e. hydraulics). It is better described as acting as a sort of low-pass filter.

So if no materials come to mind, I'd be interested in hearing of something that could filter sound very effectively while conducting heat as well.

I'd like to put the qualifier that the material is a solid, but I'd be interested really in any material with these properties just because I believe (perhaps wrongly?) that there are likely a very small number of them. Again, don't think in terms of the goal concept I mentioned regarding a computer case, this is just one step towards that thought experiment (which is likely not reasonable, or else products would be on the market right now that provide such).