Manually-designed network architectures for thermal infrared pedestrian tracking (TIR-PT) require substantial effort from human experts. Neural networks with ResNet backbones are popular for TIR-PT. However, TIR-PT is a tracking task and more challenging than classification and detection. This paper makes an early attempt to search an optimal network architecture for TIR-PT automatically, employing single-bottom and dual-bottom cells as basic search units and incorporating eight operation candidates within the search space. To expedite the search process, a random channel selection strategy is employed prior to assessing operation candidates. Classification, batch hard triplet, and center loss are jointly used to retrain the searched architecture. The outcome is a high-performance network architecture that is both parameter- and computation-efficient. Extensive experiments proved the effectiveness of the automated method.