In a context of energy transition and decarbonization, companies operating in the oil and gas sector may be more exposed to climate risks, both physical and transition related. This greater exposure may reflect in a higher cost of capital, given the risk of stranded assets, stigmatization of the sector and reduced funding. This paper seeks to study this hypothesis, applying econometric models to analyze whether climate risk, represented here by a Carbon Intensity metric (scope 1 and scope 2 greenhouse gas emissions per US$ of revenue), has a significant effect on the systematic risk coefficient (beta) of these companies. The results show that Carbon Intensity has a statistically significant positive effect on beta, contributing to the argument that greater climate risk can increase companies' systematic risk. According to the most robust model (Model 1), a 100% increase in Carbon Intensity generates a corresponding rise of 0.0608 in beta, everything else kept constant - an increase of 7.25% in relation to the average beta of the sample.