It's generally accepted by zombie experts that they're going to continue to rot, even as they shamble around the streets. What the movies fail to convey, however, is the gruesome yet strangely hilarious effect the hot sun has on a rotting corpse.
The first concern is putrefaction. Thanks to the plethora of bacteria we use in our colon for digesting plant matter, called gut flora, our bodies are ripe for decay the second our heart stops. Since heat speeds the growth of bacteria (which are plenty happy to start feasting on you once your immune system is no longer a concern) the zombie's got a looming expiration date the very second it turns.
Dead bodies bloat because of the gases created by the bacteria, meaning that in warmer areas even Abercrombie Zombies are going to start getting fat in the first few days. After a few weeks of this, the nasty, bloated zombie army is going to start doing something that is simultaneously the most awesome and disturbing thing a zombie can do: they will start exploding (CAUTION! Pictures!). The warm, moist conditions in the tropical and subtropical parts of the world (or even just summer in the temperate parts) speeds this condition, meaning a July zombie outbreak pretty much anywhere would be over in a few weeks just by virtue of the rampaging monsters bursting like rancid meat balloons.
At the other end of the heat spectrum is dry heat. If you're in Phoenix or the Sahara when the apocalypse hits, the zombies might begin to mummify in the blazing sun and heat. While the normal symptoms of dehydration are not a concern for a zombie, there is the problem of desiccation. With no reasonable means of replenishing the water in their cells, zombies walking around in the Texas heat all day are going to suffer cell damage due to direct sun exposure to their skin, and thanks to the drying effect wind has, the Southwestern dead will stumble around more and more ineffectively until, at some point, they simply drop and wait for the scavengers to come pick them up for the annual Slim Jim harvest.
So they'd better hope the outbreak happens during the winter, right? Well...