What you’re thinking about is the relation between energy, temperature, and heat capacity. When you add energy to a system (e.g. heat) the amount of energy you need to heat it up a certain amount is described by its heat capacity. If your molecules can “wiggle” (i.e. they’re multi-atomic) a portion of the energy you’re adding will go to increasing the “wiggling” rather than the mean speed of the molecules.

What we perceive as temperature is related to the mean speed of the molecules, so because molecules that can “wiggle” more will require more heat to see the same increase in mean speed as non-wiggling molecules (because some of the heat is going to increasing the wiggling) they have higher heat capacity.

It should also be mentioned that even the concept of temperature is really a statistical concept, so it doesn’t really make much sense to talk about the temperature of a single isolated molecule, or even a pair of them. Temperature as a concept starts to be fruitful to talk about in the thermodynamic limit which classically means “a whole shitload of molecules”, but (relatively) recent research suggests “a whole shitload” can be as little as 10-30 molecules. Once you go below the thermodynamic limit, we’re not really talking about the temperature of a system, but it’s energy, which is still well defined (although definitions may vary depending on context). Depending on who you ask, it can make sense to define a temperature also for single-particle systems, but at that point we’re talking about applying thermodynamic definitions that work (and are correct in the macroscopic limit) and no longer about what we classically perceive as temperature.