if a substance in a condensed state say ice is put in contact of a flame the heat from the flame Will flow into the ice by virtue of a temperature difference between them but it would not cause the temperature of ice to rise instead The condensed state begins to change into the liquid State (ice melts) at constant temperature thus the addition of heat without temperature rise is possible and this does not contradict the concept of heat as energy transferred by virtue of a temperature difference. this also does not violate energy conservation because the given heat is stored as potential energy of the molecules of the substance