A black hole would dissipate via Hawking radiation only if it doesn't absorb more energy than it emits. Large blackholes absorb more energy (cosmic background radiation) than they would emit and hence will not necessarily dissipate. From wikipedia:
"A black hole of one solar mass has a temperature of only 60 nanokelvins; in fact, such a black hole would absorb far more cosmic microwave background radiation than it emits. A black hole of 4.5 × 1022 kg (about the mass of the Moon) would be in equilibrium at 2.7 kelvin, absorbing as much radiation as it emits. Yet smaller primordial black holes would emit more than they absorb, and thereby lose mass."