One time Key Encapsulation Mechanism? For KEM's, do you only exchange a private key once via the public key encryption and then do all further encryption with this private key, or is a fresh private key sent out with each message?  The latter seems inefficient, but I could also see issues in having to store private keys for everyone.
In general you simply create a new symmetric secret key for each message. You wrap this using a trusted public key for the person holding the private key. In general you use KEM just because you don't want to encrypt/decrypt the entire message with the asymmetric key pair. Using a hybrid cryptosystem is much more efficient.

If you need to create a transport protocol you could also use KEM to establish session keys. You'd need to store those session keys for the duration of the session. Keys don't generally take a lot of resources, but you would have to keep them relatively secure, yes (at least as secure as the data you're sending during the session anyway).

In the case of a transport protocol with sessions you'd probably be better of by using an authenticated key agreement protocol though. In that case you may not need KEM.



For symmetric systems it is better to use the term "secret key" than "private key". This helps to distinguish symmetric keys from private keys that are part of an asymmetric key pair.