Yes you can get fanless notebooks (think Netbook) -- Will it be powerful enough to do your "real-time audio processing"? That's hard to say, as I'm not you and I don't know exactly what you like to do. :)
My portable computer is a "fanless" UMPC with a hyperthreaded Intel Atom in it. It runs Windows 7 Ultimate (with Aero), and constantly surprises me how well it performs with only 1GB of RAM and a 32GB SSD.
I can surf the web, watch YouTube, use MS Office, etc. I just generally stick to one or two major tasks at a time on it and it's plenty quick.
I think the problem you're facing is that regardless of when notebooks are built, they are (generally) built with the 'current' generation of processors, and because of that they (the processors) are always at a size/design that requires active cooling. Liquid cooling doesn't work well for portable computers, so they have to use a fan.
It's not until years later that the equivalent power can be miniaturized enough to run cool enough to survive on passive cooling (no fans, liquid, etc.), but by then the notebook manufactures have moved on to the next generation of CPUs, which still require active cooling.
Perhaps get a notebook, and underclock it so it doesn't get as hot?
If it doesn't NEED to be portable then there are many different manufacturers out there creating fanless PCs that are plenty powerful, you'll just have to search them out, find one(s) you like and locate a way to buy them (preferably from a place that will let you play with one for a bit before buying).
Beyond that, shopping suggestions/recommendations are against the SuperUser rules.
Hope that helps...