<p>Rayleigh-Bénard convection is a canonical problem in fluid mechanics, where an adverse temperature gradient between the opposing boundaries induces instabilities that drive natural convection. For viscoplastic fluids, a minimal perturbation is required to initiate the flow. This study presents a numerical investigation of the three-dimensional Rayleigh-Bénard convection within a cubic cavity heated from below, with lateral walls subject to a linear temperature profile. The fluid behavior is modeled using the Bingham constitutive model. The moment-based Lattice Boltzmann Method was employed as the numerical method to solve the mass and momentum transport equations, with an extended formulation to incorporate the energy transport equation using a local diffusion coefficient approach. Simulations are performed for Rayleigh numbers between 10⁴ and 10⁷. Within this range, we observed a region of Yield numbers, between 0.004 and 0.007, that fluid plastifies. Increasing the Rayleigh number led to a transition from a stationary to a chaotic state, while larger Prandtl numbers damped the fluctuations in the velocity field. Notably, the imposition of a linear temperature profile on the lateral boundaries enhances flow instability, thereby amplifying plastic instabilities as the critical Yield number is approached.</p>