The question is whether the difference between two temperature readings relates to a direct increase in energy or some sort of exponential one. For example, 11 degrees C is 1 degree hotter than 10 degrees C, how much of an energy change is this and how would this relate to 12 degrees etc. It's an interesting question but when we get our terms absolutely defined, the question disappears sadly. The reason is that energy and temperature are not related exclusively. By that I mean that two objects at the same temperature can have different energies.
The amount of energy required to heat a system can be defined as the mass of the object being heated, multiplied by the temperature change, multiplied by "the specific heat capacity" which is a measure of how much energy an object can absorb in the process of changing temperature. Thing is, this equation is dependent on mass. In other words I could have a 1 g block of ice and apply a certain amount of energy to it. A 1000 g block of ice given the same energy will not raise its temperature anywhere near as much. So temperature and heat energy, while related, don't have a simple conversion factor because it depends how much stuff you're heating and what substance you're heating.