The notion of poleward atmospheric heat transport being the fundamental factor in maintaining a pole-to-equator thermal gradient is effectively an icehouse dynamic function in practice. The presence of a strong cryospheric anomaly is essentially what upholds the thermal anomalies observed at the poles. Pretty much all observable dynamics demonstrate that we're rapidly exiting the current ice age, with atmospheric methane volumes suggesting that we've already been in an ice age termination event for almost 20 years already.

Considering that we're broadly analogous to the Mid-Piacenzian Warm Period when accounting for the present atmospheric carbon volume of >420ppm, or the Middle Miocene when accounting for the combined equivalent of ~500ppm-eq, paleoclimate analyses suggest that the planet could be anywhere between 2°c-3°c or 4°c-10°c warmer than the 1850-1900 baseline if we observed a climatic equilibrium equivalent to present atmospheric greenhouse gas concentrations. The Middle Miocene can be defined as a "cool-icehouse" or "cool-greenhouse" depending on who defined the metric (both essentially mean that only the South Pole would observe permanent glaciation, as opposed to the current cold-icehouse under which we see permanent glaciation at both poles). But it's generally accepted that atmospheric carbon volumes will continue to increase substantially in our near future. At our current rate, well more than likely be approaching 1,000ppm by the end of the century. Once we reach that stage, icehouse dynamics aren't physically possible. So essentially, nowhere gets colder as the atmospheric concentrations of greenhouse gases will essentially revert the climate to one with a substantial heat trapping characteristic.

Realistically, the current Cenozoic Quaternary is an unusually cold geological epoch. Even during our present interglacial, we're arguably observing comparatively cooler conditions when compared to geological greenhouse and hothouse conditions. Icehouse periods are actually very rare anomalies in earth's history and represent up to 20% of its entire geological record, they tend to get abruptly terminated by sudden increases in greenhouse gas concentrations (important to note that "abrupt" is usually on a scale of millenia, compared to the 150 years under which we've achieved an equivalent change).