By analyzing the historical fluctuation in temperature in 125 countries between 1950 and 2003, Dell, Jones and Olken (ungated version here) found that it does not have significant economic impacts in rich countries, but in poor countries one standard deviation increase in mean annual temperature reduces economic growth by 0.69 percentage points.
A one degree rise in temperature is associated with a 2.66 percentage points reduction in growth of agricultural outputs. in poor countries (for rich countries it is 0.22 percentage points). Also, their results show that an additional 100mm of annual rainfall is associated with 0.18 percentage points higher growth in agricultural output in poor countries and 0.16 percentage points higher growth in agricultural output in richer countries.
Furthermore, high temperature negatively impacts industrial value-added and political stability. They find that a one degree higher temperature in poor countries is associated with 2.04 percentage points lower growth in industrial output.
Overall, higher temperature is associated with political instability in poor countries. Specifically, an additional one degree change in temperature in poor countries is associated with a 2.7 percentage points increase in the probability of any change in POLITY (i.e. Policy IV index which rates political system in each country annually from –10 as fully autocratic and +10 as fully democratic). Political instability impacts factor accumulation and productivity growth. Using another dataset of leadership change, they show that a one degree rise of temperature raises the probability of leader transitions by 3.1 percentage points in poor countries.
Below is the abstract from their paper:
This paper uses historical fluctuations in temperature within countries to identify its effects on aggregate economic outcomes. We find three primary results. First, higher temperatures substantially reduce economic growth in poor countries. Second, higher temperatures may reduce growth rates, not just the level of output. Third, higher temperatures have wide-ranging effects, reducing agricultural output, industrial output, and political stability. These findings inform debates over climate's role in economic development and suggest the possibility of substantial negative impacts of higher temperatures on poor countries.
Source: Dell, Jones and Olken (2012); Panels A and B plot the change in average annual growth against the change in average annual temperature between the periods 1970-1985 and 1986-2000, for rich and poor countries respectively.