This article deals with thermo-elastic computation of heterogeneous structures containing quasi-periodic micro-structures having variable properties (geometric and/or material) using reduced order modelling. Such heterogeneous structure is extremely expensive to simulate using classical finite element methods, as the level of discretisation required to capture the micro-structural effects, is too fine. Based on the asymptotic homogenisation theory, the multi-scale technique explores the micro-macro behaviour for thermo-elasticity. Considering each integration point of the macro-structure consists of an underlying locally-periodic micro-structure, the overall problem is basically separated into a homogeneous problem defined over the macro-structure and a heterogeneous problem defined over each micro-structure. Even though the usage of multi-scale strategy helps in the reduction of numerical expense, it still deals with a full order finite element solution for the macro-problem and each micro-problem. Using a 2-fold reduced order modelling further accentuates the cost reduction and provides a robust solution in a reduced space: (i) as an offline pre-computation stage for the micro-structural problem, and (ii) as an online process that can embed adaptivity for the macroscopic problem.