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.
The book says that there is no rain on Arrakis. However, our model does suggest that very small amounts of rainfall would occur, confined to just the higher latitudes in the summer and autumn, and only on mountains and plateaus. There would be some clouds in the tropics as well as polar latitudes, varying from season to season.
The book also mentions that polar ice caps exist, at least in the northern hemisphere, and have for a long time. But this is where the books perhaps differ the most from our model, which suggests summer temperatures would melt any polar ice, and there would be no snowfall to replenish the ice caps in winter.