A semiconductor die assembly comprises a plurality of semiconductor dice in a stack. Another semiconductor die is adjacent to the stack and has a region, which may comprise a relatively higher power density region, extends peripherally beyond the stack. Conductive elements extend between and electrically interconnect integrated circuits of semiconductor dice in the stack and of the other semiconductor die. Thermal pillars are interposed between semiconductor dice of the stack, and a heat dissipation structure, such as a lid, is in contact with an uppermost die of the stack and the higher power density region of the other semiconductor die. Other die assemblies, semiconductor devices and methods of managing heat transfer within a semiconductor die assembly are also disclosed.