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Is the optimal temperature for human productivity 13°C?

A recent study attempting to quantify some of the economic costs of a warming climate argues that the optimal temperature for human productivity seems to be 13°C. As the Washington Post reports:

Culling together economic and temperature data for over 100 wealthy and poorer countries alike over 50 years, the researchers assert that the optimum temperature for human productivity is seems to be around 13 degrees Celsius or roughly 55 degrees Fahrenheit, as an annual average for a particular place.

Is this study claiming this? Is it authoritative?