Concrete is a heterogeneous material made up at mesoscale of linear elastic aggregates distributed in a mortar matrix whose behavior is time and temperature dependent. The Interfacial Transition Zone (ITZ) between aggregates and matrix also influences the overall behavior. We investigate here analytically and numerically by means of 3D simulations the creep behavior of concrete and mortar subjected to moderate temperatures at mesoscale. The numerical specimens consist in unstructured periodic meshes of polyhedral aggregates with various size and shapes randomly distributed in a box. Specific interface finite elements are introduced between aggregates and matrix to model the ITZ. Both matrix and ITZ are considered as linear thermoviscoelastic materials. Averaged stresses and strains in the matrix and aggregate phases are compared to analytical estimations obtained with classical mean-field approximation schemes applied in the Laplace-Carson space, where the ITZ are introduced via imperfect interfaces modelled with the Linear Spring Model (LSM). The effects of ITZ thickness, aggregate shape and temperature are then studied to evaluate their respective influence on mortar and concrete creep behavior.