Don't know if your context would benefit from this, would setting your CPU Frequency at a fixed, specific "low" value be acceptable, or do you need to let it range up and down to meet on-demand loads?
If a fixed frequency (power management) setting is acceptable, I invite you to review the 2nd and 4th link in the following posting:
Otherwise, once you've identified the specific process which is causing the 4.5 W consumption, you could use a system command (I think it involved "cgroups") to impose a quota on CPU usage which would constrain that power consumption. Unfortunately, I don't know anymore on the topic of cgroups. 
I don't know if there is anything helpful in this next resource, but you might want to give it a once over to see what it covers and how it recommends implementations: