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The present article pertains to the assessment of thermoelastic damping (TED) in rectangular nanoplates by incorporation of size effect within the constitutive and heat conduction relations. With the purpose of establishing size-dependent coupled thermoelastic equations, nonlocal elasticity theory and dual-phase-lag heat conduction model are utilized. By considering time-harmonic vibrations, nonclassical frequency equation affected by thermoelastic coupling is derived. By solving this equation and extracting the real and imaginary parts of damped natural frequency via some mathematical operations, an explicit expression for description of TED in circular nanoplates is obtained. With the goal of better understanding the small-scale effect on TED, a comparison is made between the results predicted by the size-dependent formulation and those determined according to classical continuum mechanics and heat conduction theories for two kinds of boundary constraints. Considerable difference between classical and nonclassical results, especially at smaller sizes, implies the necessity of incorporating small-scale effect into both structural and thermal areas. [ABSTRACT FROM AUTHOR]