From The Conversation:
We are scientists with specific expertise in climate modelling, so we simulated the climate of Arrakis to find out. We wanted to know if the physics and environment of such a world would stack up against a real climate model.
The books and film describe a planet with unforgiving sun and desolate wastelands of sand and rock. However, as you move closer to the polar regions towards the cities of Arrakeen and Carthag, the climate in the book begins to change into something that might be inferred as more hospitable.
Yet our model tells a different story. In our model of Arrakis, the warmest months in the tropics hit around 45°C, whereas in the coldest months they do not drop below 15°C. Similar to that of Earth. The most extreme temperatures would actually occur in the mid-latitudes and polar regions. Here summer can be as hot as 70°C on the sand (also suggested in the book). Winters are just as extreme, as low as -40°C in the mid-latitudes and down to -75°C in the poles.
This is counter intuitive as the equatorial region receives more energy from the sun. However, in the model the polar regions of Arrakis have significantly more atmospheric moisture and high cloud cover which acts to warm the climate since water vapour is a greenhouse gas.
There's a more detail in the article about how they created the simulation, as well as how it compares to the planet as depicted in the Dune novels (spoiler: Frank Herbert did a pretty good job!). You can explore the climate modeling yourself here as well.
Dune: we simulated the desert planet of Arrakis to see if humans could survive there [Alex Farnsworth, Michael Farnsworth, and Sebastian Steinig / The Conversation]
Arrakis [Climate Archive]