<p>Our article aims to introduce a new form of harmonic analysis within the Jacobi–Dunkl framework. We introduce the linear canonical Jacobi–Dunkl transform (LCJDT) as an extension of the linear canonical Fourier transform. Initially, we delve into the harmonic analysis associated with this transform and explore fundamental properties like the Parseval identity and inversion formula. Subsequently, we examine the LCJDT applied to the Schwartz space and tempered distribution. After, we broaden the scope of our novel findings by exploring its application to the heat equation. Next, we define the generalized translation operator associated to the proposed transform and we establish for it some important properties. Finally, using the new generalized translation operator, we define and study the convolution product related to the LCJDT.</p>