Rapeseed oil was used to develop thermoset foams via Michael addition reaction by mixing two liquid components, Michael donor and Michael acceptor. The foaming of the curing thermoset was achieved by the physical blowing agent which expanded from the reacting foam mass due to an exothermic curing reaction. The influence of the rapeseed oil-based Michael donor functionality on the foaming process and the characteristics of the obtained thermoset foams was studied. The 1,1,3,3-tetramethylguanidine catalyst’s influence on the foaming process kinetics was studied using FOAMAT equipment. The curing of the bio-based thermoset was analysed using a dielectric polarisation sensor. The morphology of the developed thermoset foam was analysed using a scanning electron microscope and the obtained foams were characterized using TGA, DSC, DMA and mechanical analysis tests. A direct correlation between the thermoset foam polymer crosslinking density and foaming reactivity, mechanical properties and glass transition temperature were determined. Obtained rapeseed oil based thermoset foams had a relatively low thermal conductivity of 33.9–35.4 mW/(m·K) which allows their use as thermal insulation material in civil engineering applications.