Recent seismic tomographic models have revealed broad, low velocity anomalies in the lower mantle beneath Africa and the central Pacific which suggest a break in the symmetry between hot and cold regions in lower-mantle dynamics. We have considered the possible impact from radiative heat-transfer, which can be described by a nonlinear temperature-dependent coefficient in the thermal conductivity, in 2-D numerical simulations. Results for Rayleigh numbers up to 106 show a strong stabilizing influence from radiative heat transfer on mantle upwellings and the production of extremely hot thermal anomalies in the interior. This nonlinearity is responsible for producing a strong attractor in the mantle convective system, which greatly simplifies its time-dependent dynamics. The possible link of the simplified lower-mantle time-dependent dynamics with polar wander is discussed. The main point here is that slow time-dependence of the huge anomalies in the lower mantle can be the main controlling mechanism of long-term rotational dynamics.