Polymers crosslinked via furan/maleimide thermo-reversible chemistry have been extensively explored as reprocessable and self-healing thermosets and elastomers. For such applications, it is important that the thermo-reversible features are reproducible after many reprocessing and healing cycles. Therefore, side reactions are undesirable. However, we have noticed irreversible changes in the mechanical properties of such materials when exposing them to temperatures around 150 °C. In this work, we study whether these changes are due to the self-reaction of maleimide moieties that may take place at this rather low temperature. In order to do so, we prepared a furan-grafted polyketone crosslinked with the commonly used aromatic bismaleimide (1,1′-(methylenedi-4,1-phenylene)bismaleimide), and exposed it to isothermal treatments at 150 °C. The changes in the chemistry and thermo-mechanical properties were mainly studied by infrared spectroscopy, 1H-NMR, and rheology. Our results indicate that maleimide self-reaction does take place in the studied polymer system. This finding comes along with limitations over the reprocessing and self-healing procedures for furan/maleimide-based reversibly crosslinked polymers that present their softening (decrosslinking) point at relatively high temperatures. On the other hand, the side reaction can also be used to tune the properties of such polymer products via in situ thermal treatments.