No, there aren't any issues with the warm or cool air affecting the batteries. The typical operating temperature range for AA alkaline batteries is between 0°F to 130°F (-18°C to 55°C).

While the temperature of the air coming out of vents can be on either end of the 0°F to 130°F range, that does not mean the batteries will get to that temperature. There are multiple layers of plastics that would further diffuse the heat and keep the batteries within operating parameters.