The stack temperature of a boiler can rise if:

The correct choice regarding why the stack temperature of a boiler can rise is that the fireside of the boiler becomes dirty. When the fireside surfaces of a boiler accumulate soot and other deposits, it creates an insulating barrier that decreases heat transfer efficiency. As a result, more heat escapes through the stack because the boiler has to work harder to generate the same amount of heat, leading to an increase in stack temperature.

In a clean boiler, the heat produced by fuel combustion is effectively transferred to the water or steam. However, when fouling occurs due to dirt and soot buildup, the efficiency drops, and the heat that should remain in the system instead gets lost up the stack, resulting in higher temperatures in the exhaust gases.

Other factors can influence stack temperatures, but in this context, the build-up of debris on the fireside has the most direct and significant impact on increasing stack temperature due to reduced efficiency in heat transfer.