A lot of people would die because of the higher temperatures in Africa and South America because they can't afford air conditioning. Meanwhile in the USA the improvement would be low because its inhabitants are evolving to adapt to colder temperatures.

Well doesn't disease thrive more in warmer weather? 

http://www.indexmundi.com/map/?v=21&r=af&l=en

The majority of the people in Africa don't live in deserts and a good portion of those that do live there have a fairly high HDI relative to the rest of Africa so it's not impossible to get your hands on some air conditioners or water ... 

Climate change is happened regardless of whether it is down to us or the planet, debate over if the human race is contributing it is the thing in debate and honestly, I'm not sure how anyone can say we aren't having an impact of some kind. The planet doesn't burn this much stuff naturally, it doesn't dump countless tonnes of waste into landfills, it doesn't have to dreg the ocean for unbiodegradable plastic and it doesn't over fish.

It depends on the diseases themselves ... 

Cold and Flu viruses often thrive in cooler weather ... 

while large parts of Canada and Siberia could become farmland with a mild increase of ww mean temps this is also an unpredictable risk

permafrost soil stores away extremely large quantities of methane and other organic material which could quickly be released into the air/converted to carbondioxide/methane once they thaw and bacteria can do their work -> further temperature increase

and then theres the problem of methane ice reserves in the oceans - all that's needed is a few degrees K of a temperature rise to destabilize several large reserves, which would result in a "blow out" of the gas into the atmosphere further exacerbating the temperature increase (we have good evidence that this happened several times in the past and lead to extreme temperature spikes)

-> the potential gain is nowhere worth the risk

That's mainly because people are crowded around eachother more in colder weather but those are nothing compared to west nile virus, lyme disease, cholera, malaria, dengue and probably more. Bacteria in general, thrives in warmer weather. 

Yes, because only deserts are hot.

https://en.wikipedia.org/wiki/Kano#Climate

2nd biggest city in the most populated country of Africa, an average high of over 100F in April in a country with a GDP per capita below $2800.

And why are we talking only about Africa?

You don't know that when climates are nonlinear systems ... 

that's right, it's an "educated guess" - the difference is that your scenario of a stable positive change is merely a "hope"