What causes the lack of steam pressure of my espresso Saeco machine?

This does sound like a thermostat failure. Does the light still come on after the steam switch is pressed, and some time is given for it to heat up? If not, again, this does sound like a thermostat failure. There are two thermostats on the top of the boiler. The steam thermostat should be the one closest to the pump. Check to see if the wires on top of it go to the steam switch to be sure.

It sounds like your thermostat is functioning to a certain point, if the light is coming on. Your understanding of the thermostats is correct, they usually work, or don’t. But I have seen them slowly fail. When the upper limit is reached, the circuit “opens”, and the heating element stops heating the water. Some of the newer models have a reset button on top, but those either work, or don’t. The thermostat in your machine is probably simply failing. There are two, and it sounds like if the machine brews coffee normally, it might be the steam thermostat. You can also check the heating element for current leakage. This can happen if there is corrosion inside the boiler that wears through the coating on the element. Unplug the machine, and place one lead of a multimeter on the top of the heating element, and the other on the metal of the boiler. There should not be any continuity. If there is, you have current leakage due to corrosion inside. This can also cause less than optimal heating. Plus, it can trip your circuit breaker.

The thermostat is supposed to be either “open” or “closed”, but there are cases where it is only partially working. You may replace to see if that corrects the issue. Another possibility is that the tip of the pipe in the boiler is partially clogged with scale. Try a descale using this trick. After running some solution through the brew head and steam wand, unplug the machine. Remove the water tank with the solution, and the drip trays. Invert the machine for 10-15 minutes. Then, sit upright and replace the tank with the solution. Allow it to heat up, and run some solution through the steam wand and brew head. Now, unplug and repeat. This may remove some scale build up at the top of the pipe in the boiler, and solve your issue.