Poly(lactic acid) (PLA) and biosourced polyamide (PA) bioblends, with a variable PA weight content of 10–50%, were manufactured by melt blending in order to improve the behavior of PLA against thermal degradation. The effect of reactive extrusion on the thermal performance of PLA within bioblends was analyzed. The reactive extrusion was made by means of the addition of a styrene-acrylic multi-functional-epoxide oligomeric reactive agent (SAmfE), with the commercial name of Joncryl. Four parameters were considered in order to study the thermal behavior of bioblends against thermal decomposition: the onset decomposition temperature, the shape and temperature interval of the thermal decomposition patterns, the activation energy of the thermal decomposition, and the evidence leading to the most probable mechanism. The latter was determined by means of three evidence: standardized conversion functions, y(α) master plots, and integral mean error. It was shown that reactive extrusion of PLA as well as PA incorporation to the polymer matrix of PLA were responsible for an increase in the onset decomposition temperature of 10.4 °C. The general analytical equation (GAE) was used to evaluate the kinetic parameters of the thermal degradation of PLA within bioblends for various reaction mechanisms. It was shown that the random scission of macromolecular chains is the best mechanism for both untreated and treated PLA by means of reactive extrusion. It was shown that reactive extrusion together with higher content of PA resulted in an increased protective effect against the thermal degradation of PLA as demonstrated by an increase in activation energy of 60 kJ/mol. It was found that there is a relationship between the increase in activation energy and the increase in the onset decomposition temperature when using reactive extrusion. The improvement of the thermal stability of bioblends by means of reactive extrusion was explained by an increase in the complex viscosity from 980 to 2000 Pa·s at 0.06 rad/s and from 250 to 300 Pa·s at 630 rad/s for bioblend containing 30% of PLAREX and by a finer dispersion of PA within the PLAREX matrix. Results from DSC were not conclusive regarding the compatibility between both phases.