Why does raising the temperature affect the mass of dissolved solute?
For many (though not all) solids dissolved in water, solubility increases with temperature. The increase in kinetic energy that comes with higher temperatures allows the solvent molecules to more effectively break apart the intermolecular forces of the solute molecules.

For many salts and some gasses there are visual representations of solubility variation with temperature called a solubility curve, for which the units are $\frac{\mathrm{g~solute}}{\mathrm{100~g~solvent}}$. I could not find one for $\ce{KOH}$, but the Wikipedia page for $\ce{KOH}$ lists the solubility of $\ce{KOH}$ at various temperatures, and it is clear the trend is that it is more soluble at higher temperatures.

As a result of Le Châtelier's principle, substances that release heat upon being dissolved tend to dissolve better in colder water. This accounts for gasses and some salts.

You should note, however, that although $\ce{KOH}$ does evolve a large amount of heat upon being dissolved, as the concentration of $\ce{KOH}$ increases, the process becomes less exothermic, and eventually near the saturation point it becomes endothermic (it becomes less favorable to dissolve more $\ce{KOH}$), which explains why it is more soluble at higher temperatures.