Marangoni thermocapillary convection and its contribution to heat transfer during boiling has been the subject of some debate in the literature. Currently, for certain conditions, such as microgravity boiling, it has been shown that Marangoni thermocapillary convection has a significant contribution to heat transfer. Typically, this phenomenon is investigated for the idealized case of an isolated and stationary bubble resting on a heated surface, which is immersed in a semi-infinite quiescent fluid or within a two-dimensional cavity. However, little information is available with regard to Marangoni heat transfer in miniature confined channels in the presence of a cross flow. As a result, this article presents a two-dimensional (2D) numerical study that investigates the influence of steady thermal Marangoni convection on the fluid dynamics and heat transfer around a bubble during laminar flow of water in a miniature channel with the view of developing a refined understanding of boiling heat transfer for such a configuration. This mixed convection problem is investigated under microgravity conditions for channel Reynolds numbers in the range of 0 to 500 at liquid inlet velocities between 0.01 m/s and 0.0 5m/s and Marangoni numbers in the range of 0 to 17,114. It is concluded that thermocapillary flow may have a significant impact on heat transfer enhancement. The simulations predict an average increase of 35% in heat flux at the downstream region of the bubble, while an average 60% increase is obtained at the front region of the bubble where mixed convective heat transfer takes place due to forced and thermocapillary flow.