The walls of ice chest are made of an insulating materials. If the chest is closed, warm air outside the chest cannot flow over the ice meaning that little heat is lost through convection.
The rest of the heat is lost through conduction, or heat flowing directly through the walls of the ice box. It does not mean that heat is not lost at all from the ice chest. It does get lost, but the rate is very slow.
Here, thermal energy transfer means the heat from outside flows into the object and makes it hot, The ice chest prevents that from happening and melts itself in order to keep the object cool.
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