Thermal energy attempts to equalise itself across its environment. So heat moves from something hot (with a lot of thermal energy) to something cold (with little thermal energy).
However thermal energy is conducted only slowly though certain substances. Newspaper (and, just as importantly, the stationary air trapped between the layers of newspaper) acts as a partial thermal barrier because heat can only be conducted slowly across it.
When there's ice cream inside the newspaper, the equalisation of thermal energy means that heat is seeking to get inside the package, but is partially prevented form doing so by the thermal barrier of poorly conducting newspaper (+ air). So the ice cream remains cool.
When there's fish and chips inside the package, the equalisation of thermal energy means that heat is seeking to get out of the package but, again, the wrapping largely prevents it from doing so, the the fish & chips remain hot.
Chris