It sounds not a trivial task for a high-school-er. I will try to help, but I wouldn't be able to go in depth with you.
We can say heat with a transformer is from a part of loss. First, I searched "transformer" on WikiPedia. In that page, search (^f) for "heat", and found what causes the heat of a transformer: Winding joule losses, Hysteresis losses, Eddy current losses, and Stray losses. And, it seems those are not only the source of heat, but major losses as well. Meantime, magnetic induction may need to be considered separately from heat and losses.
Winding joule losses: Current flowing through a winding's conductor causes joule heating due to the resistance of the wire. As frequency increases, skin effect and proximity effect causes the winding's resistance and, hence, losses to increase.
Hysteresis losses: "Each time the magnetic field is reversed, a small amount of energy is lost due to hysteresis within the core, caused by motion of the magnetic domains within the steel. According to Steinmetz's formula, the heat energy due to hysteresis is given by.."
Eddy current losses: Eddy currents are induced in the conductive metal transformer core by the changing magnetic field, and this current flowing through the resistance of the iron dissipates energy as heat in the core.
Stray losses: Any leakage flux that intercepts nearby conductive materials such as the transformer's support structure will give rise to eddy currents and be converted to heat.
Besides the main losses, Radiative losses may not contribute much to heat;
Radiative losses: There are also radiative losses due to the oscillating magnetic field but these are usually small.
Answer to your question, first step: We can intuitively tell:
Secondary Power (I_sec x V_sec) = [Primary Power (I_pri x V_pri)] - Losses
This does not feel like easy formula to expand. So, I googled "transformer loss calculation".
Out of many, this one, How to Calculate Transformer Losses, suggests empirical method, while some engineers developed tools, Spread Sheet for Transformer Losses Calculation.
Meantime, Schneider Electric has good documents to read. This and this cover wide area of transformer knowledge.
