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Despite many approaches proposed in the past, robotic climbing in a complex vertical environment is still a big challenge. We present here an alternative climbing technology that is based on thermoplastic adhesive (TPA) bonds. The approach has a great advantage because of its large payload capacity and viability to a wide range of flat surfaces and complex vertical terrains. The large payload capacity comes from a physical process of thermal bonding, while the wide applicability benefits from rheological properties of TPAs at higher temperatures and intermolecular forces between TPAs and adherends when being cooled down. A particular type of TPA has been used in combination with two robotic platforms, featuring different foot designs, including heating/cooling methods and construction of footpads. Various experiments have been conducted to quantitatively assess different aspects of the approach. Results show that an exceptionally high ratio of 500% between dynamic payloads and body mass can be achieved for stable and repeatable vertical climbing on flat surfaces at a low speed. Assessments on four types of typical complex vertical terrains with a measure, i.e., terrain shape index ranging from -0.114 to 0.167, return a universal success rate of 80%-100%.