Is it permissible to use high-consumption electric heaters in government-funded university housing, knowing that they are prohibited, and is expiation required for that if the answer is in the negative?

Using an electric heater without the permission of the granting authority is an infringement on the rights of others. You must stop doing so, resolve not to repeat it, and seek absolution for this action by referring to the university dormitory officials. If this entails paying for electricity consumption, then it must be paid to the responsible authority. If that is not possible, then dispose of it for the general benefit of Muslims or for the poor.