Calculus-based physics is easier to understand
Mathematics required for the study of statistical mechanics / thermal physics
Depending on what your elementary school class is focused on, you will need a math background below:
Basic probability theory : An idea of permutations, probability distributions, mean and variance, etc. Depending on how statistical the class becomes, you may need more.
Partial differentiation : For the thermophysical side, a solid understanding of partial derivatives is of crucial importance. While this is usually taught in a multivariable calculus class, it can be easily learned if you understand basic derivatives but don't underestimate their usefulness.
Fundamental series extensions : Approaches are everything. If you can't find the exact answer, a good approximation is the next best thing. You can extend simple polynomials and trigonometric functions. Stirling's approximation is also used quite often.
For the physical side of things:
Basic kinematics : Understanding introductory physical ideas about force, momentum and energy. Basic systems such as harmonic oscillators.
Quantization : Again, this depends on how deep the class is, but it can be good to have an idea of quantization in physics. eg: de Broglie relationships
This is not meant to be exhaustive, but rather a list of things that I remember remembering being useful. Some basic chemistry can also be useful, but probably not necessary. I would highly recommend speaking to the professor teaching it to get a good idea of what to expect.
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