There are many open-source tools available for solving heat transfer problems. These include:

• FEniCS: a Python-based software library for solving partial differential equations using the finite element method.
• Elmer: an open-source multiphysics simulation software that includes a module for solving heat transfer problems.
• OpenFOAM: an open-source software for computational fluid dynamics that includes capabilities for solving heat transfer problems.
• MFEM: an open-source library for solving partial differential equations using the finite element method.
• Project Chrono: an open-source physics-based simulation framework that can be used to simulate a wide range of dynamic systems, including thermal analysis and multibody dynamics.
• Code_Aster: an open-source software for finite element analysis that includes thermal analysis capabilities.
• FreeFEM++: an open-source software library for solving partial differential equations using the finite element method.
• deal.II: an open-source software library for solving partial differential equations using the finite element method.
• GetFEM++: an open-source C++ library for solving partial differential equations using the finite element method
• Netgen and NGSolve: open-source software libraries for solving partial differential equations using the finite element method.
• Gmsh: an open-source 3D finite element mesh generator that can be used to create high-quality, unstructured meshes for solving partial differential equations, including heat transfer problems.

All these software packages are open-source, and they provide a wide range of features and capabilities, and can be used to solve a wide range of heat transfer problems. Some are written in Python, others in C++,Fortran, and all have active user communities that contribute to the development and maintenance of the libraries, making them reliable and robust options.