  Heat transport in turbulent thermal convection increases with the thermal
forcing, but in almost all studies the rate of this increase is slower than it
would be if transport became independent of the molecular diffusivities -- the
heat transport scaling is slower than the mixing-length (or `ultimate')
scaling. In configurations driven by either thermal boundary conditions or
internal heating, thermal boundary layers instead lead to a boundary-limited
(or `classical') scaling. With net-zero internal heating and cooling in
different regions, mixing-length scaling can occur because heat need not cross
a boundary. We report numerical simulations in which heating and cooling are
unequal, as in various natural systems, at a Prandtl number of unity. As
heating and cooling rates are made closer, the scaling exponent of heat
transport varies from its boundary-limited value to its mixing-length value.
