Sterling engines: Discussions

As far as the working principle is concerned, the air in a closed cylinder(closed by a diaphragm, with a piston rod passing through it), is heated. the air next to the heated wall of the cylinder gets its density reduced , rises and pushes the piston upwards. And simultaneously the cooler air makes contact with the heated wall, and the process repeats.

speed of the crankshaft increases periodically as the heat supplied is constant, and as the temperature of the working fluid rises continuously.

As i see it the working of this engine is quite similar to that of a dc series motor (speed increases continuously).

Now what would happen if the temperature of the working fluid reached a saturation point, and if heat was still supplied to it. would the cylinder explode ? is this why this engine has no practical applications ? whats your say ?