Fiber-based endoscopes are promising for minimally invasive in vivo biomedical diagnostics. Multicore fibers offer high resolution imaging. However, to avoid image deterioration induced by inter-core coupling, significant spacing between cores is required, which limits the active image guiding area of the fiber. Thus, they suffer from low light collection efficiency and decreased signal-to-noise ratio. In this paper, we present a method to increase the collection efficiency by thermally expanding the cores at the facet of a multicore fiber. This expansion is based on the diffusion of doping material of the cores, thus the fiber's original outer diameter is preserved. By enlarging the core diameter by a factor of 2.8, we increase the intensity of the transmitted light by a factor of up to 2.3. This results in a signal-to-noise ratio increase by a factor of up to 4.6 and significant improvement in the image contrast. The improvement increases with increasing working distance but is already prominent for as small working distance as 0.5 mm. The feasibility of the method is proved experimentally by lensless single-shot imaging of a test chart and incoherent light reflected from clusters of microbeads. The demonstrated approach is an important tool especially in imaging of biological specimens, for which phototoxicity must be avoided, and therefore, high collection efficiency is required.