Soft actuators have received great research attention because of the recent rise of soft robotics. However, these actuators could perform only relatively simple deformations (such as bending, twisting, etc.) for manipulation, limiting their functionality. Here, we develop highly responsive and shape adaptive soft robotic heaters which not only can achieve large degree of deformation but also can grab and heat objects of three-dimensional (3D) curvilinear surfaces. With intentionally synthesized and selected materials for device fabrication, a U-shaped soft robotic heater exhibits a deformation angle of more than 860° and a curvature of 4.0 cm-1 at a very low voltage of 2 V, and its curvature can quickly reach 1.31 cm-1 within 6 s. Moreover, the device can also function as a stable heat source with temperature of 203 °C upon actuation, demonstrating a maximum energy efficiency of 7.44% as a heater. Importantly, the soft robotic heaters can deform to enclose 3D curvilinear surfaces with pressure to enable intimate contact for more effective heat transfer. The unique utility of the soft robotic heaters is illustrated through the heating of objects of various 3D shapes, showcasing their potential applications in soft robotics, advanced thermal therapy, food handling and processing, etc.