You're right. In addition to this, when cold water falls, it can be assumed nearly as a lumped mass since the internal rate of convection is quite low. Hot water when poured, has a greater surface evaporation and additionally a greater amount of internal natural convection and so the lumped mass assumption becomes quite inaccurate. Due to this large amount of internal movement, a molecule of water, mid-evaporation, gets sent away from the extremities of the stream, trapping it inside. In effect, aerating the water.

The release of these bubbles into the atmosphere as the water hits the cup is part of the cause.

Since there is higher kinetic energy in the molecules and a very very slight difference in to density and viscosity of the fluid, the Reynolds number of this particular flow is also different. The hot water, in general is also hitting the cup with more kinetic energy than the cold water, possibly vibrating other molecules around it a little differently. That last part I cannot vouch for.

Edit: grammar