In EteRNA, the melting temperature can be thought of as the temperature at which there would be enough energy to pull the structure apart from it folded structure to a linear form.
In general, a higher melting temperature indicates higher stability in your structure.
However there is a caveat which is that the algorithm in EteRNA that calculates the melting temperature is not very good. It is only accurate to the nearest 10 degrees. Therefore, you should be careful in trying to use the information from the melting temperature.
Melting temperature relates to the free energy (What is Free Energy?) in that as free energy goes down, melting temperature goes up, as both are measures of stability.