The hotter the water, the more compounds will be dissolved. Increasing the water temperature increases the temperature of the compounds themselves, which in turn increases their solubility. Water cannot exceed 100°C at sea level, so this places a limit on the compounds which can dissolve into the brew. At low temperatures, water won’t dissolve all of the flavours we usually get with hot water. This can be seen with the stark difference between cold brew and hot brewed coffee. Cold brewed coffee has much less sweetness. It is these sweet, heavier organic molecules hot water readily dissolves. Additionally, the quality and desirability of those compounds change drastically across different coffees and roast styles.
The longer the water and coffee are in contact, the greater the number of soluble compounds that can be dissolved. Temperature can be somewhat interchanged with time. This is why cold extractions require hours to reach completion, and hot brews only seconds or a few minutes to taste good. As with above, the swap isn’t linear as there are some compounds that just will not dissolve in cold water.