As renewable energy is becoming the major resource in future power grids, the weather and climate can have a higher impact on grid reliability. Transmission expansion planning (TEP) has the potential to reinforce the power transfer capability of a transmission network for climate-impacted power grids. In this paper, we propose a systematic TEP procedure for renewable-energy-dominated power grids considering climate impact (CI). Particularly, this paper develops an improved model for TEP considering climate impact (TEP-CI) and evaluates the reliability of power grid with the obtained transmission investment plan. Firstly, we create climate-impacted spatio-temporal future power grid data to facilitate the study of TEP-CI, which include the future climate-dependent renewable power generation as well as the dynamic line rating profiles of the Texas 123-bus backbone transmission (TX-123BT) system. Secondly, the TEP-CI model is proposed, which considers the variation in renewable power generation and dynamic line rating, and the investment plan for future TX-123BT system is obtained. Thirdly, a customized security-constrained unit commitment (SCUC) is presented specifically for climate-impacted power grids. The reliability of future power grid in various investment scenarios is analyzed based on the daily operation conditions from SCUC simulations. The whole procedure presented in this paper enables numerical studies on power grid planning considering climate impact. It can also serve as a benchmark for other studies of the TEP-CI model and its performance evaluation.