The simple answer is "look at the heat capacity".

For a simple mono-atomic gas, the heat capacity is $\frac32 R$ per mole. For a diatomic gas, it's $\frac52 R$ - because two new modes (rotations) appear that can be excited and contain energy ... after which the equipartition principle does the rest.

Note that the diatomic gas does not have a heat capacity of $\frac72 R$ as you would expect if rotation about its axis or vibration along its axis were involved in storing energy. The reason is that these modes are quantized - and that the thermal energies are insufficient to excite a reasonable fraction of the molecules into the higher energy state. Thus the assumptions that go into the equipartition principle don't apply - and the heat capacity reflects that.

If you have more complex molecules, you can get certain bending modes that will be excited more easily - these are capable of acting as reservoirs of thermal energy, and will affect the heat capacity. For such gases the answer would be "yes".

Note that for water, a significant additional complication is the formation of hydrogen bonds between molecules at lower temperatures; this affects the heat capacity of water in the liquid form in particular (heat capacity changes with temperature for liquid water; and to a lesser degree, for steam). According to [this table](http://www.engineeringtoolbox.com/saturated-steam-properties-d_457.html), the heat capacity of steam actually increases with temperature. This suggests that the vibration modes become more important as temperature goes up. This is even more evident in the [heat capacity for liquid water](http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html): while it is initially almost flat at 4.2 kJ/Kg/K, around 260°C it rises to 5 kJ/kg/K and then quickly to 10 kJ/kg/K around 250 °C.

There is a good write-up of all this on [wikipedia](https://en.wikipedia.org/wiki/Heat_capacity#Diatomic_gas) - where it is stated that the energy spacing of the vibrational modes is inversely proportional to the reduced mass of the molecule: this implies that "heavy" diatomic molecules (like $\rm{Br_2}$) have their vibrational mode excited, while the lighter ones do not. An idealized plot of the heat capacity of hydrogen as a function of temperature (from http://theory.physics.manchester.ac.uk/~judith/stat_therm/node81.html which credits P. Eyland from the University of New South Wales ... but I could not locate the original) looks like this:

[![enter image description here][1]][1]

showing that the heat capacity increases first when the rotational modes are accessible for equipartition of energy, and that vibrational modes follow at some (much) higher temperature.


  [1]: https://i.sstatic.net/jfxiS.gif