Is there any cooling-off period that should be considered before processing new visit visa application?

The short answer is no, there is no cooling-off period before processing a new visit visa. Generally, you can apply for another visa as soon as your previous application was rejected. There are few special cases where depending on the reason for rejection you will not be able to re-apply for a specific amount of time, but these cases are rare. Although, for those who already have a visit visa, they must complete their duration of validity before applying for another visit visa.