Hi ggofpac
If the MEL states that there are no maintenance actions required then there is no requirement to go back on stand. You will have to ensure that you satisfy the requirements of the MEL for the particular issue you have and complete any Operational Procedures that are associated with it.
The captain will annotate the tech log by writing the issue in the defects column, and in the Action Taken column, something along the lines of "Dispatched IAW (in accordance with) MEL REF. 1.2.3.4 with their signature.
(I suppose there may be the chance that the Operational Procedure could include actions that require engines to be shut down but without an MEL in front of me I can't check if there are any that are like this)
Hope that helps
Pro Spin