In bug 49087, and in other places, it has been suggested that the partial logging of thanks actions visible to date is not helpful and should be either expanded or removed.
In order to prevent aggregation of thanks received on a per-edit basis (ala Like or +1 button), it is unlikely that logging will be expanded to include edits etc. In general, thanks are not intended to be public displays of appreciation for a particular edit, and should remain semi-private or entirely private between two editors.
Currently, the English Wikipedia's request to hide Thanks logs from the default view was fulfilled, making the logs something a user needs to actively know about and seek out specifically. This works for that community, while potentially letting others see the logs as well.
If we do turn off all public logging of thanks actions, we should consult with all the communities that currently use Thanks, and gauge their reaction.