I think most waxes just get thicker till they are eventually solid like butter.
This would be because waxes are a mixture of many different length hydrocarbons typically, all with different melting points. So whilst there is no distinct freezing/melting point, it is actually happening over a wider temperature range. I'm sure the rate of change of temperature would slow at the point where melting begins until it finishes, and because it happens over a wider temperature range might actually be more useful in a real life situation.
However, compared to filling bottles with water, it does seem like a painful and expensive exercise (and somewhat typical of the industrial system's over complicated and needlessly expensive solutions to a simple problem)
It would be interesting to see how water behaves against wax or indeed any mixture of oils (olive oil? coconut oil?), given that it would be both unlikely and undesirable to take advantage of the latent heat between solid and liquid states, given the change in volume that goes with it. At least with coconut oil, if the bottle broke it would smell really good (in my opinion)!