It is likely either the armature bearings or the pump impeller but check the cooling fan (if it has one), as well. It's not that bad a job to separate the motor from the pump to inspect/replace the impeller. The armature bearings are another story and it may be a toss up whether or not to replace the motor or have it rebuilt. Any bearing problems I've encountered have all resulted in a lower pitched grinding/rattling sound.
Sounds like something, when cold is interfering but as it warms and expands is OK. Just my two cents.
Thanks for your reply. I will try your suggestions.