The temperature will be the average of 10 C and 20 C which is 15 C.
Energy is transferred from faster moving molecules to slower moving molecules, and the result is the average of 15°C. This is just another temperature problem where you add something hot to a cold liquid and you have to calculate the final temperature. Since the energy given up by the hot coffee = energy absorbed by the cold coffee, the mass of the two fluids is the same (each is 1 cup) and both are coffee so the specific heat is the same, you get T hot - Tfinal = Tfinal - Tcold and then you solve it, you get T final = (T hot + Tcold) / 2 which is simply the average of the hot and cold temperatures.
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