This repo contains two "papers" I wrote in high school to get a hang of special relativity and thermodynamics (not the interaction between them, sadly). The main point where it differs from typical textbooks is the focus on a rigid mathematical or logical basis as opposed to experimental proof.
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Kinetic theory. This is a 45-page introduction to thermodynamics in Russian, covering topics from the definition of temperature to entropy. Most laws are rigorously proved, including the equipartition theorem and Maxwell's distribution. The proofs are written in a style that should be quite tractable for someone who knows just basic calculus.
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Relativity. This is a 7-page inference of the formulae for relativistic momentum and relativisic energy. I avoid postulating definitions and then checking their validity, instead opting for a rigid derivation from basic axioms.