It is often stated that daily variations in cellar temperatures are more damaging to wines than consistently higher temperatures. As far as I know empirical evidence for this is lacking, but that is not to say it is necessarily wrong.
One possible mechanism could be that the resulting pressure variations pump out oxygen-depleted air, and suck in air that is richer in oxygen – or something analogous if the bottle is stored in the correct horizontal position and the cork soaked in wine. Unfortunately, I find it difficult to get a handle on how likely an explanation that might be.
However, the reason most often proffered is that the pressure variation caused by the temperature changes can loosen the cork, making it more likely to leak. It is a lot easier to do a quick calculation to establish the plausibility of this explanation. It turns out that a 10ºC variation in temperature will result in a force of around 100g acting on the cork – see the bottom of this post for the workings. That is, for example, the force equivalent to the weight of a smallish apple.
A better way of understanding it might be to push on some kitchen scales with a finger until they read 100g. You can then compare that with the force you need to get a cork moving when extracting it with a cork screw. Judge for yourself, but I find it totally implausible that the 100g force would shift most corks – however slightly, and however many times that force is applied. Perhaps very old corks that a cork screw would push into the bottle might be affected, but I am still not totally convinced of that either.
Ah, but you say there are also pressure variations outside the bottle due to the weather, and when added to the pressure variations due to temperature inside the bottle they could be a lot more significant. Well, above are shown the atmospheric pressure variations measured at the National Physical Laboratory for 2015. It turns out that the pressure variations due to weather are about the same order of magnitude as those due to 10ºC temperature variation – again, see my workings below – and they are lot less frequent than every day, so they will not make that much difference.
So, in conclusion, I don’t know of any evidence for daily temperature variations being worse for wines than consistently high temperatures. That does not rule out the possibility, but it also seems unlikely that those temperature fluctuations will loosen corks.
If you’re up for it, here’s…
The science bit
Gay-Lussac’s law says that for gases at a constant volume, pressure is proportional to temperature. Here the temperature must be measured on a scale where zero means absolute zero, so we will use Kelvin for temperatures. Room temperature is around 300 K, and we are looking at a temperature variation of 10 K, which is the same as 10ºC. Thus the relative change in temperature is 10/300 – around 0.03 or 3%.
Atmospheric pressure is approximately 100,000 N per square meter, and according to Gay-Lussac the relative change in pressure is the same as the relative change in temperature. So the absolute change in pressure is 100,000 x 0.03 = 3,000 N per square meter. (At this point you might also like to note that the atmospheric pressure variations shown above are also of the order of 3%.)
That pressure change acts on the area of the cork, which is about 1 cm, or 0.01 m, in radius. The area of the cork is 3.14 x 0.01 x 0.01 = 0.000314 square meters. 3000 N per square meter acting on an area of 0.000314 square meters gives a force of 3000 x 0.000314 = 0.94 N, which is approximately 100 g force.
Edit 24/07/19: It later occurred to me that although liquids generally expand much less than gases, the volume of wine is a lot greater than the ullage in the bottle, and that the wine expanding may significantly compress the air, and thus increase the pressure by more than calculated above. So I redid the calculation to take account of the above effect, and also with some other improved assumptions. Overall, including the effect of using a specified temperature change of 15-25ºC, a high-fill ullage volume, a pressure at 15ºC of 1 bar, and an expansion coefficient I found for white wine, the change in force on the cork would be 160 g. This reduces to 115g for a low-shoulder ullage. So the force is larger than originally estimated, but not one so much greater that it invalidates my general conclusions. I’m not going to publish my workings here, but let me know if you would like to see them.