A packaged semiconductor device includes a package substrate, a first semiconductor device on the package substrate, and at least one second semiconductor device that extends on and partially covers the first semiconductor device. A heat dissipating insulation layer is provided as a coating on the first and second semiconductor devices. A conductive heat dissipation member is provided, which extends upwardly from the heat dissipating insulation layer and on portions of the first and second semiconductor devices. A protective member is provided on the package substrate, to cover the first and second semiconductor devices and the conductive heat dissipation member. This protective member includes a first covering portion, which covers an upper surface of the conductive heat dissipation member.