The average random molecular velocity (whose direction is, in a stochastic sense, evenly distributed in space and whose direction changes constantly through collisions) corresponds to temperature in e.g. kinetic gas theory. This has nothing to do with the macroscopic velocity which has a direction. So yes, the difference between the velocity that can be associated with temperature and the macroscopic velocity we talk about in fluid/continuum mechanics is the randomness or non-randomness of their direction. Which is a very important distinction, though.
This means that something does not move when it gets really hot because the displacement the velocity due to thermal motion is on the average zero. The thermal velocity that can be assigned to every molecule/atome changes its direction constantly through collisions with other molecules/atoms.
For the same reason, something does not get hot when it is moving - because the random velocity of the single particles does not change.
As has been pointed out in the comments, it might be worth to also mention the scale seperation of those velocities. To quote Pirx from the comments:
As an aside, the average molecular velocity in an ideal gas is of the order of the speed of sound in that gas. Thus, for practical, every-day situations, the velocity of the gas molecules is much, much higher than the macroscopic velocity of the gas flow.