Rising temperatures and increasingly frequent heatwaves are among the most prominent and well-documented manifestations of climate change. While recent studies show that extreme heat reduces firm productivity, the implications on market power remain largely unexplored, which represents an important research gap as shifts in market power can carry substantial welfare implications. Our study aims to fill this gap by examining the impact of temperature extremes on market power and the resulting welfare implications. Our empirical analysis draws on detailed firm-level balance sheet and geo-location data from ORBIS, combined with high-resolution weather information, covering 12 European countries from 2000 to 2020. We begin by analyzing how temperature extremes affect firm market shares and market concentration. The results provide strong and robust evidence that extreme heat increases local market concentration by shifting market share from smaller to larger firms. In addition, extreme heat reduces firm productivity while increasing the average markup. The effects are heterogeneous across firms: productivity losses are concentrated among small firms, whereas increases in markups are observed among large firms. To quantify the impact on welfare, we develop a stylized heterogeneous firm model à la Melitz (2003), which explicitly incorporates the heterogeneous effects of climate shocks on firm productivity across different firm sizes. To capture how these heterogeneous impacts lead to market share reallocation and changes in firm markups, we adopt a variable elasticity of substitution (VES) framework which allows for endogenous markup following Atkeson and Burstein (2008). The quantification exercise shows that the climate change productivity shock we observed from 2000 to 2020 leads to a welfare loss equivalent to 0.124 percent of manufacturing sector GDP in Europe, with substantial variation across countries. More importantly, if we ignore the role of reallocation and variable demand elasticity, we can misstate the welfare cost of climate change.