Chocolate can be refrigerated without deterioration. However, unless it is carefully wrapped, if it is kept in the refrigerator for a long time, it will pick up other food odors. When you remove it from the refrigerator, let it come to room temperature before unwrapping it. This will prevent moisture from condensing on the chocolate. Also, the chocolate will be harder and more brittle until it warms up to room temperatures.
Cocoa is less sensitive to temperature changes than chocolate.
However, the fine grains of the cocoa powder will tend to clump at higher temperatures. Since cocoa usually comes in cans, it is not likely to be affected by high humidity. If you are not sure that the can is sealed tight, it would be best to seal the container in a plastic bag or transfer the cocoa powder to another air tight container.