Background
The authors -- a mathematician and a statistician -- introduce their study by stating that "malaria is the main public health problem in the area of Burundi," citing Protopopoff et al. (2007) and the World Health Organization (2005), while further noting that malaria is responsible for some two million clinical cases that result in more than 15,000 deaths each year, including 50% of all hospital deaths of children under five years of age.

What was done
Nkurunziza and Pilz employed Bayesian Generalized Additive Models (GAMs) to assess the impact of an increase in temperature on malaria transmission, which in addition to monthly maximum and minimum temperature data utilized monthly rainfall and humidity data, as well monthly malaria morbidity data for the period 1996-2007, all of which were obtained for each province of the country.

What was learned
Overall, in the words of the two researchers, "the results of the GAMs show that an increase in the maximum temperature will cause an increase in minimum temperature," and they say that "the increase in the latter will result in a decreasing maximum humidity, leading to a decrease in rainfall." And these results, as they continue, "suggest that an increased temperature will result in a shortening of the life span of mosquitoes (due to decreasing humidity) and decrease in the capacity of larva production and maturation (due to decreasing rainfall)," so that ultimately "the increase in temperature will not result in an increased malaria transmission in Burundi," which result is said by them to be "in good agreement with some previous works on the topic," citing as examples WHO, WMO, UNEP (2003), Lieshout et al. (2004) and Thomas (2004).

What it means
In one final statement on the matter, Nkurunziza and Pilz write that in regions with endemic malaria transmission, such as Burundi, "the increase in temperature may lead to unsuitable climate conditions for mosquitoes survival and, hence, probably to a decreasing malaria transmission [italics added]."

References
Lieshout, M.V., Kovats, R.S., Livermore, M.T.J. and Martens, P. 2004. Climate change and malaria: analysis of the SRES climate and socio-economic scenarios. Global Environmental Change 14: 87-99.

Protopopoff, N., Herp, M.V., Maes, P., Reid, T., Baza, D., D'Alessandro, U., Bortel, W.V. and Coosemans, M. 2007. Vector control in a malaria epidemic occurring within a complex emergency situation in Burundi: a case study. Malaria Journal 6: 1-9.

Thomas, C. 2004. Malaria: a changed climate in Africa? Nature 427: 690-691.

WHO. 2005. Strategie de cooperation de l'OMS avec les pays, Republique du Burundi 2005-2009.

WHO, WMO, UNEP. 2003. Climate Change and Human Health -- Risks and Responses: Summary. Geneva, Switzerland.