Very cold weather reduces the capacity of any battery, as the cold slows down chemical reactions needed to generate electricity.
Hot weather (including a battery located in a hot engine compartment, unlike the Genesis) can weaken the individual plastic cells of a flooded cell battery, especially when a sudden impact occurs like hitting a hole in the road, causing sudden battery damage if the separate battery compartments rupture and chemicals start intermingling between the cells. In this kind of damage, a car will usually keep running (due to alternator, etc), but not be able to start again once shut off.
AGM batteries have much better resistance to hot weather damage, because the battery liquid chemicals are contained in many different Glass Matt compartments that can generally handle more heat stress without battery failure.
Some flooded cell batteries are available in both north and south versions. The north versions have thinner cell walls for maximum cranking power. The south batteries have thicker cell walls (at the expense of slightly lower cranking power) in order to reduce the likelihood of physical damage as the result of heat and sudden impact. Larger batteries like the H8 and H9 are usually pretty well built and have lots of cranking power, due to their size.
Starting in 2015, Hyundai Genesis comes standard with AGM batteries, but they can also be used for replacement batteries of previous models.