So I have stayed in Schengen zone for 25 days last month.
My visa is expiring soon. Now I want to go for another trip in two months and apply for another Schengen visa for 10 days.
Is there a problem in there? Is there a "cool-down" period between two Schengen visas or it doesn't matter?
There is no cool-down period between visas but a 90 days in any 180 day maximum stay rule, which does amount to a kind of cool-down period between stays.
Note that this rule also applies across multiple visas, which is why no other restriction is really necessary. It's not a problem for you since you have only stayed for 25 days so far but if you had already used up your 90 days and wanted to travel before the end of the relevant 180-day period, you could not get a new visa.
