In this study, a new flexible hybrid shape memory alloy composites (SMAHCs) with a polydimethylsiloxane (PDMS) matrix containing a shape memory alloy (SMA) of a hybrid Basalt/Kevlar fiber 3D woven composite is developed. The SMAHC is implanted into a glass fiber/PDMS composite laminate in a modular manner to study the stiffness of composite plates in response to temperature. The variable stiffness theory of the SMAHC is derived, and the influence of SMA parameters on the stiffness of the SMAHC is analyzed. A three-point bending test is performed to determine the stiffness of the composite plates at multiple temperature points in the form of Joule heat driving the composite plates. The stress and temperature distributions of the composite plate are analyzed in Abaqus under a temperature-displacement coupling setting. The results shows that the SMAHC stiffness is negatively correlated with SMA fiber diameter and positively correlated with SMA fiber volume fraction. With an increase in driving temperature, the stiffness of the composite plates tends to decrease. When the end temperature of the austenitic phase transformation is reached, the high-modulus austenitic SMA slightly increase the stiffness of the composite plate. The stiffness improvement is more significant when the SMAHC is placed in the middle area of the laminate and the SMA is located in the tension area. This study may provide a reference for the design of variable stiffness SMAHC for plate composite structures.