The interplay of yield stress and elasticity on the temperature field and heat transfer rates in tube flow of elastoviscoplastic (EVP) fluids is investigated in this paper. The constitutive structure of the EVP fluid obeys a linear combination of the Phan-Thien-Tanner model for viscoelastic fluids and the Bingham model for viscoplastic fluids. The momentum and energy equations are solved asymptotically under constant wall heat flux. The fluid behavior is governed by the Weissenberg Wi and the Bingham N numbers.