That is correct. In general, warmer climates are more stable than cooler climates.
You can see that in the sharp Dansgaard-Oeschger climate fluctuations which punctuated the last glaciation, compared to the relative stability of the Holocene interglacial.
Here's a paper (one of many) about Dansgaard‐Oeschger events:
https://www.nature.com/scitable/knowledge/library/abrupt-climate-change-during-the-last-ice-24288097/…
I link to that paper, and to other related resources, on my website, here:
https://sealevel.info/learnmore.html?0=d-o#d-o…
As you can see, D-O events are globally synchronous, but much sharper in the northern hemisphere than the southern:
https://sealevel.info/curryja_2017-02_figure-22_dansgaard-oeschger_cycles2.png…
You can also see that in the relative stability of temperatures in the tropics, compared to the large "Arctic amplification" seen at high northern latitudes, as well as the large seasonal & diurnal temperature variations there.
One of the reasons that warmer climates are more stable is that is that Planck Feedback is ∝ T⁴, so the warmer the climate gets, the stronger that negative (stabilizing) feedback is.
https://sealevel.info/feedbacks.html#planck…
Another reason is that warmer climates tend to have higher absolute humidity, because warm air holds more moisture than cold air. That increases latent heat transport, which cools the surface in daytime and warms it in evenings when the dew point is reached, both of which moderate temperature swings.
Additionally, there are apparently negative (stabilizing) feedbacks involving clouds, which limit temperature rise in the tropics:
https://sealevel.info/feedbacks.html#tropicalsst…