Focusing on tubular reactors with continuously distributed side injections, a general procedure to evaluate the operating mode able to reproduce the performance of a given semi-batch reactor is worked out. Namely, such operating mode is expressed as axial profiles of feed flowrate and temperature of the cooling/heating medium inside the reactor jacket. This transformation procedure, previously limited to isothermal reactors, is extended here to non-isothermal systems. The process performance (selectivity and conversion) of the original discontinuous reactor are fully reproduced using the continuous intensified reactor, while its productivity remains a degree of freedom. Notably, like in the isothermal case, the transformation procedure is kinetics-free, i. e. the knowledge of the reaction kinetics is not a precondition. As case study, a copolymerisation reaction is considered to demonstrate the potential of the method. Even though any SBR feed policy could be considered when applying this methodology, the optimal feed policy of the semi-batch reactor evaluated according to the so-called "power feed" procedure is examined considering the reactor non-isothermal. Afterwards, the proposed transformation method is applied and the performance of the two systems, discontinuous and continuous, are comparatively evaluated. Finally, given the practical difficulties associated with continuously distributed side injections, a discretisation approach is proposed based on the use of discrete lateral feeds and more realistic reactor configurations.