Heap Inspection is about sensitive information stored in the machine memory unencrypted, so that if an attacker performs a memory dump (for example, the Heartbleed bug), that information is compromised. Thus, simply holding that information makes it vulnerable.
One can mitigate this by storing such sensitive information in a secured manner, such as a GuardedString object instead of a String or a char array, or encrypting it and scrubbing the original short after.
For more information, see this CWE (describes C/C++ but same relevancy for Java).
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