I have a Pentair Amerlite that has a label stating the bulb it came with is a 120V 400W R40. It doesn't have a warning stating that a bulb exceeding the wattage listed should not be used, like most light sockets state the maximum wattage allowed.

The instruction manual shows the replacement parts and lists 300W, 400W and 500W options. The only place I see anything related to wattage is in the replacement instructions where it indicates you will need a new gasket and a lamp, for proper type and wattage, see table 1. Table 1 lists the 3 different wattages. It's as if the housing is the same in the diagram and just the bulb is different.

The pool store guy sold my wife a 500W bulb because they were out of the 400W ones and told her it should work, but I have my reservations.

Will a 500W bulb work in the 400W housing without overheating and tripping the overheat sensor or burning out prematurely?

I don't want to find out the hard way....