By introducing four displacement functions, the governing equations of the threedimensional thermoelasticity of two-dimensional hexagonal quasicrystals are decoupled into two uncorrelated problems. Two higher-order displacement functions are introduced to represent the general solutions, which are eighth-order and fourth-order, respectively, for the two problems. By taking a decomposition and superposition procedure, the general solutions are further simplified in seven cases in terms of six quasi-harmonic displacement functions. To show the application of the general solutions obtained, a closed form solution is obtained for an infinite space containing a penny-shaped crack, subjected to a uniformly distributed temperature at the crack surface.