Adding to
@cmason1957's advice, a warm temperature is important only during fermentation. The colder it is, the slower the yeast eat. My cellar is typically 58 F in December, January, and February and that's where my wines rest. That said, I have fermented whites at 58 F, which lasted 3+ weeks. If you're a beginner, target 70 to 80 F, until you become comfortable with the wine making process.
Colder temperatures aid in clearing, as the saturation point of all materials in the wine reduces as the temperature drops. The lower the saturation point, the more solids will drop. There is a recent thread on cold stabilization/crashing, that offers more detailed information regarding temperature, although that is geared towards tartaric acid. Search for "cold stabilization".
Most (maybe all?) of the fining agents cause the suspended particles to clump together. As the clumps get heavier with size, they drop lower in the wine, until they settle. Stirring the sediment back into suspension provides more raw material for clumping, so the process occurs faster. As long as the directions for the fining agent(s) are followed, they will work. Stirring the sediment means it works faster.
And as others have mentioned, do nothing and the wine usually clears anyway. Kits use fining agents as 99.9% of beginners want the wine in the bottle so they can drink. Experienced wine makers want the same exact thing, but most of us have learned patience.