Cold water coming out of hot tap - problem?
The mixing valve of the washing machine can let cold water into the hot line. Also single valve lavatories and kitchen faucets. You can tell which one is allowing the flow by turning off the cut-off valve to that point of use.

EDIT

This is only occurring when the hot water line is shut off. It is not a fault condition. It happens all the time with the single handle sink mixing valves.