In a fantasy world I am constructing, a planet goes through regular, but extreme temperature cycling. Roughly every 500 years, the planet begins to heat or cool, dependent on its current temperature. Transition periods between high and low temperatures are relatively short (~20 years). If plotted, this would resemble a square wave.

The amplitude of this wave is significant, with peak temperatures similar to those of the Eocene thermal maximum (27° C), and trough temperatures similar to the last glacial maximum (9° C). This would mean that the planet also goes through intense hydrological cycling as ice sheets freeze and thaw, coastlines drift, and weather patterns change. Thus warm periods also correspond to wet periods, and cold periods correspond to dry periods.

Given this harsh oscillation, most species on Earth would not do well. The equator would remain relatively stable from what I can tell, resulting in similar conditions to what we would see on Earth, but living beyond even 30° N/S would likely require extreme migratory patterns or specific adaptations to accommodate the climate shifts. Thus I am wondering **what adaptations and behaviors would allow organisms to survive away from the equator?**

To answer this question, consider both plants and animals. It may be assumed that all organisms have developed some sort of sense to allow them to predict when these climate shifts will occur a few years in advance to accommodate any behavioral shifts or morphological changes that need to occur. Additionally, even though this is a fantasy world, assume that the only explicitly magic effects visible is the ability to slowly redistribute body mass, and the natural generation of heat within specific kinds of rocks. 

Assume that the first ability takes longer given greater physiological changes, for instance a complete change of body plan might take a week, whereas superficial changes like changes in coloration patterns might only take a few minutes. Greater changes additionally require significant brain power to accomplish. This brain power cannot be sacrificed during the transition. Assume that the ability of stones to generate heat is limited to some volcanic rocks always feeling slightly warm, and a small subset of these stones being hot enough that they would be uncomfortable to touch, but would not results in damaging burns on contact.

My own research into the subject suggests that species that can fly and have significant thermal insulation (birds) would do well in this environment given their high mobility and ability to survive the cold. Small mammals like foxes, rodents, and cats would also do well in this environment due to their resistance to temperature shifts, as well as their low energy demand. Grazing animals like deer and bison may also be able to tolerate the shift given the ability of grasses to survive cold and hot conditions, as well as their own natural tolerance for ranges of environments.

Plants would likely undergo extreme blooming periods during warming cycles to reseed rehydrated and thawing regions, but it seems that many temperate would be able to persist with small variations in sap chemistry. An interesting point of note is that deciduous trees may not lose leaves in the cold phases as the solar flux remains constant.