My Samsung Chromebook from 2012 has an ARM processor, solid state storage, and no fans. It is pretty slow by today's standards though.
I think several companies make cases for the Intel NUC boards that radiate the heat away and have no fans, too.
My Samsung Chromebook 3 gets a touch warm but never uncomfortably so like my 2012 Retina MacBook, which lets you really feel it when your code is inefficient. (Granted, the Chromebook is a lot less powerful)