Furfuryl alcohol (FA) is a biobased monomer derived from lignocellulosic biomass. The present work describes its polymerization in the presence of protic polar solvents, i.e., water or isopropyl alcohol (IPA), using maleic anhydride (MA) as an acidic initiator. The polymerization was followed from the liquid to the rubbery state by combining DSC and DMA data. In the liquid state, IPA disrupts the expected reactions during the FA polymerization due to a stabilization of the furfuryl carbenium center. This causes the initiation of the polymerization at a higher temperature, which is also reflected by a higher activation energy. In the water system, the MA opening allows the reaction to start at a lower temperature. A higher pre-exponential factor value is obtained in that case. The DMA study of the final branching reaction occurring in the rubbery state has highlighted a continuous increase of elastic modulus until 290 °C. This increasing tendency of modulus was exploited to obtain activation energy dependences (Eα) of FA polymerization in the rubbery state.