The "Kyoto Box," named after the United Nations' Kyoto Protocol that seeks to cut emissions of greenhouse gases, is aimed at billions of people who use firewood to cook.
Costing 5 euros ($6.60) to make, it can also make it easier to boil polluted water.
"We're saving lives and saving trees," the Kyoto Box's developer Jon Boehmer, a Norwegian based in Kenya, said in a statement.
The FT Climate Change Challenge was backed by the Financial Times, technology group Hewlett-Packard, which sponsored the award, and development group Forum for the Future.
The other four finalists were a garlic-based feed additive to cut methane emissions from livestock, an indoor cooling system using hollow tiles, a cover for truck wheels to reduce fuel use and a "giant industrial microwave" for creating charcoal.
A statement said that Boehmer would carry out trials in 10 countries, including South Africa, India and Indonesia. He would then collect data to back an application for carbon credits.
The United Nations is discussing giving credits to developing countries that preserve tropical forests, which soak up carbon as they grow. Those credits could then be traded.
Many countries are looking for cheap green ways to stimulate economies mired in recession. More than 190 nations have agreed to work out a new U.N. climate pact to succeed Kyoto at a meeting in Copenhagen in December 2009.