•New analytical solution for thermocapillary convection in self-rewetting fluids (SRF) layers in a microchannel.•Interface surface tension equation of state modeled with parabolic dependence on temperature.•Lattice Boltzmann (LB) method based on central moments for simulation of SRFs developed and validated.•Thermocapillary flow patterns in SRF layers shown to be markedly different from normal fluid layers.•Effect of surface tension sensitivity parameters, fluid thickness ratio, thermal conductivity and viscosity ratios studied. Self-rewetting fluids (SRFs), such as aqueous solutions of long-chain alcohols, exhibit anomalous quadratic dependence of surface tension on temperature having a minimum and with a positive gradient. When compared to the normal fluids (NFs) that have negative gradient of surface tension on temperature, the SRFs can be associated with significantly modified interfacial dynamics, which have recently been exploited to enhance flow and thermal transport in various applications. In this work, first, we develop a new analytical solution of thermocapillary convection in superimposed two SRF layers confined within a microchannel that is sinusoidally heated on one side and maintained at a uniform temperature on the other side. Then, a robust central moment lattice Boltzmann method using a phase-field model involving the Allen-Cahn equation for interface tracking, two-fluid motion, and the energy transport for numerical simulations of SRFs is constructed. The analytical and computational techniques are generally shown to be in good quantitative agreement with one another. Moreover, the effect of the various characteristic parameters on the magnitude and the distribution thermocapillary-driven motion is studied. The thermocapillary flow patterns in SRFs are shown to be strikingly different when compared to the NFs: For otherwise the same conditions, the SRFs result in eight periodic counterrotating thermocapillary convection rolls, while the NFs exhibit only four such vortices. Moreover, the direction of the circulating fluid motion in such vortical structures for the SRFs is found to be towards the hotter zones on the interfaces, which is opposite to that in NFs. These features are found to be sustained even as the interfaces deforms in simulations. By tuning the sensitivity coefficients of the surface tension on temperature, it is shown that not only the magnitude of the thermocapillary velocity can be significantly manipulated, but also the overall flow patterns as well. It is also demonstrated that the thermocapillary convection can be enhanced if the SRF layer adjacent to the nonuniformly heated wall is made relatively thinner or has higher thermal conductivity ratio or has smaller viscosity when compared to that of the other fluid layer. The peak Marangoni velocity is found to be increased by a factor of 2 by doubling the dimensionless quadratic surface tension sensitivity coefficient and by about an order of magnitude as the fluid thickness ratio is changed from 1/3 to 3.