Stirling are extremely simple engines, which as long as mechanics are sound, solely rely on a certain amount of temperature difference, to obtain the expansion/contraction of air needed.
When the entire construction is more evenly heated that phenomen is reduced, which often is seen in poorly designed homebuilds with insufficient cooling.
Once "overheated" the sole solution is to let it cool, to get it back to full efficiency...or simply apply more heat to the heat cap.
On a model like this, adding more heat would most likely cause serious issues, as several parts on there only tolerate a certain amount of heat.