Your understanding of the magical system and its effects on fire seems plausible so far. Here are some additional factors and effects to consider when dealing with the energy source and its interaction with fire:
Energy conversion: The energy used to mimic fire might not have the same conversion efficiency as a real fire. Depending on how you want your magical system to work, the energy-to-heat conversion could be more or less efficient, affecting the intensity and duration of the fire.
Temperature control: The magical fire might have the ability to regulate temperature more accurately than a natural fire. This could be useful for various applications such as forging, cooking, or other controlled processes.
Ignition point: Depending on how your magical system works, the energy might have a different ignition point than a natural fire. This could affect the types of materials that can be burned or how easily the fire can be started and extinguished.
Color and appearance: The appearance of the magical fire might differ from that of a natural fire. It could have unique colors, brightness, or other visual properties.
Smoke and emissions: Since the magical fire doesn't create any actual elements, you may decide that it doesn't produce smoke or other emissions typically associated with combustion. This could be an important distinction between magical and natural fires in your world.
Interaction with other elements: Consider how your magical fire interacts with other elements in your magical system. For example, does the fire have unique properties when combined with magical water or air? Can it be used to create new types of energy or magical effects?
Magical fire control: The users of this magical system might have a higher level of control over the fire they create compared to natural fires. They could potentially shape, direct, or manipulate the fire more easily, making it a versatile tool or weapon.
Exhaustion of the energy source: Depending on the rules of your magical system, the energy source used to create the fire might become depleted or exhausted over time. This could have consequences for the availability and sustainability of the energy source and impact the story or world-building.