The toric code model is the simplest model featuring quantum topological order, i.e. long-range entanglement, in its ground state. It was originally defined in two space dimensions (2D). This model is known to loose topological order at any finite temperature in the thermodynamic limit. The reason is the thermal proliferation of point-like topological defects (anyons). A 3D version exists that has a finite-temperature phase transition. However, long-range entanglement is not present at any finite temperature in this model. Only the 4D version is known to exhibit true topological order at small but finite temperature. Recently a variation of the 3D toric code model, known as the 3D fermionic toric code, was proposed that features true long-range entanglement at finite temperature. In this internship, we will explore the physics of topological order at finite temperature working on the examples of the 3D toric code and the 3D fermionic toric code. In particular, we will try to understand the notion of true thermal topological order by contrasting the two models. As a follow up, we could also study the bosonic toric code model in 4D.