I am going to take a different approach from DavePhD and Floris.

"Hot"ness or temperature more generally is a thermodynamic idea, and can't really be applied to an individual molecule. Dave and Floris have avoided the issue by simply comparing and energetic molecule with a less energetic one, and that is reasonable, but it makes their answers frame-of-reference dependent. Presumably they are working in the rest frame of the macroscopic samples from which they drew their test particles. All very reasonable.

I'm going to make my usual argument about scale of inspection. 

A mole of hot water is more massive than a mole of cold water because when examined at the human scale you can't differentiate the kinetic energy of the molecules from any other form of internal energy (and energy is mass). The scale of this change is that figured by Floris.

Examined at the level of a single molecule than each particle has the same mass--properly defined as the Lorentz scalar formed by contracting it's four-momentum with itself: $m^2 = \bar{p}\cdot\bar{p}$--and the fast molecule has more kinetic energy--$T = E^2 - m^2 = (\gamma - 1)m$--than the slow one. This approach follows the conventions of particle physics where we don't use the term "relativistic mass".

The upshot is a "Yes and no" answer, or perhaps a "You're not quite asking the right question". 

Is the molecule of hot water heavier than that of cold water?
Would the following sentence be idiomatic and correct?


  At the conference, she became acquainted with more than 20 scholars,
  exhibiting excellent networking skills.


I was thinking saying something like "connected to more than X scholars".  I'm just not sure which expression better conveys the meaning that she took the initiative to approach those scholars and got to know them.
