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I'm interesting whats the coolant in Stirling engine that can take
off quickly Q that was brought to the system so that pressure drops
for giving the work.

The heat input for a Stirling engine is usually a flame or other high temperature, the cold end by forced air or preferrably a water cooling jacket of some sort. Mechanical energy is removed for useful work by the engine. The pressure fluctions in a Stirling engine is not a simple but complex change as the fluid (air or other gasseous medium) is being heated in one area and cooled in another at the same time.
PS It is called a Stirling engine with an "i" not an "e."