Why does entropy increase when the difference in temperatures is decreased?
Consider two tanks of water. One hot, one cold.

You open a valve between the two. The temperature between the two bleeds, and the hot tank loses entropy, and the cold tank gains entropy. However, entropy is also gained just by this process happening, as it would be impossible to force the 'cold' tank to retransfer the heat back to the 'hot' tank.

Also, you must consider something else. The two conjoined systems now have more molecules than either system alone, increasing the 'randomness' as a whole. Considering dice, it's like having two sets of two, then one set of four. The set of four has more possibilities than just the set of two.