One way to define temperature is via statistical physics. It is a quantity used to describe an equilibrium distribution of possible states via Boltzmann factor. Given a total energy of a classical system
$$E(x_1,\ldots,x_N, p_1, \ldots p_N)$$,
where $x_1 \ldots x_N$ are the position coordinates, and $p_1 \ldots p_N$ are the momentum coordinates. The probability of the system being in a particular state in now given proportional to
$$P(x_1,\ldots,x_N, p_1, \ldots p_N) = Z^{-1} e^{-E(x_1,\ldots,x_N, p_1, \ldots p_N) / (k_B T)}$$
In classical system of particles, it almost always is the case, that the total energy is a sum of kinetic energy and velocity independent potential energy.
$$E(x_1,\ldots,x_N, p_1, \ldots p_N) = V(x_1,\ldots,x_N) + \sum_i^{N} \frac{p_i^2}{2m} $$
We could play with the idea of dividing the total kinetic energy of the system to three components, translation kinetic energy, rotation kinetic energy and vibrational kinetic energy with help of suitable coordinate system
$$E_{tot} = E_{trans} + E_{rot} + E_{vib}$$,
where the translation kinetic energy is given by
$$E_{trans} = \frac{P^2}{2M}$$,
where $P=\sum_i p_i$ and $M=\sum_i m_i$. Now, we can speculate, that the probability for the system center of mass having a certain velocity V is roughly proportional to
$$P(V) \approx e^{-\frac{1}{2}MV^2 / (k_BT)}.$$
Given that, the total kinetic energy is huge compared to $k_BT$ (which is just fractions of an eV in room temperaure), we can conclude that if we find a system with large V, this is a non-equilibrium system and temperature is defined only on equilibrium systems. Therefore, the definition of temperature is ill-defined here.
Ok, this was just purely formal. In practice, one does not consern one-self with such formalities, but just moves to center-of-momentum coordinates or something similar. For example, it is standard practice in molecular dynamics simulations to first initialize the velocities of atoms according to Maxwell-Boltzmann distribution, but then to remove total momentum and total angular momentum to prevent excess drift and rotation. The number of particles is usually so large, that one does not even consider the fact that there are few degrees of freedom less, than one would get just by based on particle number. An exception is few particle systems, where one needs to switch to reduced mass coordinates.
