Keratoconus is a severe eye disease that leads to deformation of the cornea. It impacts people aged 10-25 years and is the leading cause of blindness in that demography. Corneal topography is the gold standard for keratoconus diag-nosis. It is a non-invasive process performed using expensive and bulky medical devices called corneal topographers. This makes it inaccessible to large populations, especially in the Global South. Low-cost smartphone-based corneal topographers, such as SmartKC, have been proposed to make keratoconus diagnosis accessible. Similar to medical-grade topographers, SmartKC outputs curvature heatmaps and quantitative metrics that need to be evaluated by doctors for keratoconus diagnosis. An auto-matic scheme for evaluation of these heatmaps and quantitative values can play a crucial role in screening keratoconus in areas where doctors are not available. In this work, we propose a dual-head convolutional neural network (CNN) for classifying keratoconus on the heatmaps generated by SmartKC. Since SmartKC is a new device and only had a small dataset (114 sam-ples), we developed a 2-stage transfer learning strategy-using historical data collected from a medical-grade topographer and a subset of SmartKC data-to satisfactorily train our network. This, combined with our domain-specific data augmentations, achieved a sensitivity of 91.3% and a specificity of 94.2%.