In really hot climates the engine will know the difference between the 5w30 and 0w40.
I had a mechanic tell me once "You need thicker oil, then the oil leak may stop because your engine is older the 0w 40 is no good as it is designed for tight tolerance motors" (Mechanic of over 30 years experience).
I asked what I should get, he said you need something a little thicker and said to get like a 15w 30.
I call up 2 oil companies and speak to the tech department, and they say the mechanic is ignorant and not up to date with how oil works. He is just going of what worked 30 years ago.
A 0w 40 weight oil is heavier/thicker than a 5w 30 or even a 15w 30. So to need a 'thick oil' to stop oil leaks, a 15w 30 would of actually been thinner and counterproductive.
The 0 weight means the engine will be better protected at start up as 0w is thinner than the 5w and much more so than 15w. Also important to understand when you turn your engine on it is cold, so it will run off that first number, the sooner that oil gets through your engine the less wear it will take as a lot of an engines wear happens during cold start up because parts start moving without being properly lubricated. If you think about it in an extreme example, its metal on metal at start up before the oil gets through, so the sooner the oil gets through the less wear you get prolonging the engines life. So a 0w will always be better than a 5w and much much better than a 15w. Wherever a service manual is called for a 5w or a 10w or even a 15w... the lower you can get (0w in this case) the better as mentioned already, the oil gets to your parts sooner to prevent the wear happening on cold start ups.
This is why you should not use a 20w if the service manual calls for a 15w. Trying to push that weight through the engine on cold start up, you are asking for premature wear. So having a higher W number is not recommended but lower than what is called for can only be better not worse.
The last number in this case 30 or 40 is the viscosity of the oil at running temperature.
Important to note that 30 or 40 does not mean thicker than 0w at start up. That does not designate the thickness. Any oil (cook with oil etc) once oil is heated up it will be thinner than what was in the bottle. Same with the engine oil, it may be a 0w 40, but the 40 is operating temperature and therefor thinner than the initial 0 (when its sitting in the bottle it is in its thickest state). However, 40 at that thin operating temp will be thicker than the 30 in the 5w 30 at operating temperature.
In hot climate, a 30 or 40 weight (top end, operating temperature) shouldn't be too thick for application (like say a 50 or more which can cause lowered economy in tight tolerance vehicles)
So I would personally use the 0w 40 over the 5w 30.
Better protection at start up as it is thinner and gets to the engine parts sooner when most of the wear happens on your vehicle, and slightly thicker oil at running temperature when the engine is working hard, thus keeping it more protected there than the thinner 30.
Also worth noting most of the companies technology/research seems to go into the newly developed 0w 40 weight oils so the additives and everything else in the oil will probably be better as well as the base stocks being better over the other weight oils. The reason I mention that (which was mentioned to me by mobil and castrol oil companies) is because I was looking for a 50 weight oil thinking that a 50 weight will protect even more at higher temp than a 40 for regular use, but the 0-50 or 10-50 whatever they were (dont remember) were not as good as the 0w 40 versions because more of their research goes into the 0w 40 (more people need 0w 40 than a 50) so though it was 'thicker' its all the stuff/technology that goes into that oil that is not as good as the 0w 40.
So unless you need the thickness of a 50 oil, the 0w 40 will protect your engine better (going of what castrol said to me) is that the engines oil protecting ability lies in all the stuff that is in the oil. If it was just oil that protected the engine, then you could just stick vegetable oil in your car and be done with it.
So an oils ability to protect, clean etc the engine is based on how much of the stuff (additives etc) are left in the engine. The longer you go between oil changes, the more of that stuff is used up;. That is why oil changes need to happen, not because theres no oil in the car but because all the stuff in the oil designed to protect, clean, coat, etc the engine have been used up and no longer in the oil. The oil is essentially just a medium for those things to work effectively.
So those things (additives and stuff) are better in 0w 40 weight oils as that is where most of their research goes.
If you plan on selling the car like most people, then I doubt it will matter to you personally what you use. But if you want to have the insurance policy for your peace of mind, get the 0w 40 not the 5w 30 it is the better oil and will protect better at cold starts and operating temp. From memory I'm pretty sure they told me the 0w 40 will also last longer between oil changes because it has more of the additives etc in the oil. That is why there just is no logic in changing an oil early, only change it when the additives designed to clean/protect etc the engine are starting to get low, not before, and generally the 0w 40 has more of them than the 5w 30 and thus the oil change intervals are longer (more stuff in oil to do the job longer).