The way that Vibranium works is by absorbing incoming energy and then allowing it to be dispersed through redirection.
Superman's Strength is variable but ranges from around a few tons to infinite.
Assuming material sciences still apply to Vibranium the energy is being stored in the shield as moving atoms. It can then be assumed that the Vibranium is just capable of holding its shape at higher heat ranges than other metals and that there is some key in releasing it in a given direction.
There are 2 stategies that Superman can apply to break the shield...
1. Differential heating and cooling. The differences in the atoms could theoretically cause fractures and shatter the shield.
2. Just keep hitting it or heat vision it. Eventually the capacity to "hold" the energy will be too much and the shield will melt/be destroyed.
The first method may not work just because the redirecting and taking in the energy implies an ability to transfer energy quickly and so it would either take a massive difference or it just would never be enough.
The second method depends on the maximum capacities of the shield and Superman. Superman's heat vision can get through his invulnerability which means it is producing extreme heat, because Superman can live inside stars. Can Vibranium take the heat of stars or greater? I don't think it can, but I don't think there was ever a stated limit, but there are examples of it being destroyed with less than Nuclear force. Superman can produce Nuclear forces thus he can destroy Vibranium. So can a lot of other Superheroes.
Hypothetically, it could be possibly to prevent destruction though if one were fast enough and able to release the energy faster than it built up to its limit. So Flash with the Shield could make it impossible to destroy, but under normal conditions, a lot of superheroes could easily destroy it despite what a lot of authors want to write in various comics ^.^