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In this paper, the recent development of extended consecutive-interpolation 4-node quadrilateral element (XCQ4), which goes beyond certain limitations of conventional methods, is further employed to study dynamic and static thermoelastic fracture problems. In particular, static stress intensity factors (SIFs) and transient dynamic responses of two-dimensional (2-D) stationary cracks in elastic solids under thermal and thermal-mechanical loadings are investigated. In addition, simulation of quasi-static crack propagation under thermal-mechanical loading condition is also performed. To precisely capture the singularity and discontinuity of temperature, heat flux, and displacements due to the presence of crack, the unknown field variables of mechanical displacements and temperature are approximated in terms of the XCQ4 framework by different enrichment strategies, which include either the use of the conventional branch functions or the new ramp function associated with Heaviside function. Only adiabatic condition is considered on the crack surfaces. For quasi-static crack growth analysis, the maximum hoop stress criterion, which is also valid for thermo-elastic fracture mechanics, is adopted. For transient crack analyses, the inertial effect is taken into account for the interaction integral in the consideration of DSIFs. Through eight numerical examples for thermoelastic fracture problems, the validity of the XCQ4 is confirmed by a comparison of the obtained results to those derived from different approaches in previous studies. In addition, the accuracy, performance, and superior advantages of the XCQ4 over standard extended finite element approach are also demonstrated. [ABSTRACT FROM AUTHOR]