Entropy is logarithmic with respect to degrees of freedom, and since degrees of freedom is (usually but not always) proportional to the energy of the system, the temperatures of the tea and of the room will approach each other faster when the difference between them is greater, but the heat exchange will slow down when the temperatures are similar.

EDIT I meant to say that entropy is proportional to degrees of freedom, which is logarithmically related to heat energy (except in some weird cases). Anyway, the conclusion was right :-)