Motivated by several applications such as thermal management of electronic components, the design and modeling of heat exchangers, etc. this work presents an efficient monolithic finite element strategy for solving thermo-fluid-structure interaction problems involving a compressible fluid and a structure undergoing small deformations. This formulation uses displacement variables for the structure and velocity variables for the fluid, with no additional variables required to ensure traction, velocity, temperature and heat flux continuity at the fluid-structure interface. The use of an exact tangent stiffness matrix ensures a quadratic rate of convergence within each time step. The robustness and good performance of the method is demonstrated by applying the proposed strategy to a wide spectrum of problems pertaining to steady/transient, two/three-dimensional/ axisymmetric problems involving conjugate heat transfer. In particular, it is shown that the proposed formulation yields good results even when the fluid is almost incompressible.