Methods for improving heat transfer at the interface between the internal reactor wall and mesh media containing microfibrous entrapped catalysts (MFECs) and/or microfibrous entrapped sorbents (MFESs) are described herein. Improved (e.g., more rapid) heat transfer can be achieved using a variety of approaches including increasing the contacting area of the interface between the mesh media and the reactor wall so that more contacting points are formed, enhancing the contacting efficiency at the contacting points between the mesh media and the reactor wall, increasing the number of contact points between the mesh media and the reactor wall using fine fibers, and combinations thereof.