Why does entropy increase when the difference in temperatures is decreased? From the Wikipedia article about Entropy (Source view via The Internet Archive):

In irreversible heat transfer, heat energy is irreversibly transferred from the higher temperature system to the lower temperature system, and the combined entropy of the systems increases.

If entropy were a measure of disorder, or randomness, or the amount of information needed to describe the microstates of a system, then it seems that when the difference in temperatures is high, entropy should be high. A temperature gradient in the systems is a form of ‘disorder’ hence should be a sign of higher entropy.
So why does entropy increase after the heat transfer, as the combined system approaches a uniform temperature? It seems to me like a state with less randomness or disorder.
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.