Unless you are doing a very high load of API requests or transactions, the reason for high CPU usage is usually the mining proof-of-work, which is superfluous in a private/permissioned chain.
If you start a new chain with the parameter target-adjust-freq=-1 (this requires a recent version, for which it is also the default), this problem should not appear.
Please let us know if that does help and we'll look into it further.