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 2D numerical simulations. Results for Rayleigh numbers up to 10(6) 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 mechanism controlling long-term rotational dynamics.