More frequent and intense drought and heat events imply increased multi-risks for urban green infrastructure (UGI) and their ecosystem services. To tackle this challenge, a conceptual drought and heat risk assessment framework has been developed. This study operationalizes the framework by providing a methodology that supports decision makers in their assessment, and selection of risk reduction alternatives. The methodology overlays two main procedures of the assessment: risk analysis and risk evaluation. Within the risk analysis, the risk system is delineated, from the drought and heat hazards, to the vulnerabilities of UGI entities, ecosystem functions (EF), and ecosystem services (ES). Urban parks, creeks, and lakes are used as exemplary UGI to derive biophysical system variables as so-called endpoints. A multi-layer approach is applied to translate the endpoints into an information system comprising descriptor, attribute, and indicator layers. The assignment of attributes and indicators to descriptors is based on a literature search. Hazard attributes are then linked with vulnerability indicators to derive risk indicators. A lane-based approach is adopted to interrelate indicators, and to identify the key indicators of the cascading nature of the system. The indicators "Net leaf-air temperature" and "Leaf net CO2 assimilation" are determined as key indicators with 10 linkages each. As for the risk evaluation, a guideline is set to support the selection of methods for the multi-criteria evaluation. Based upon, methods such as the Analytical Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are deemed especially applicable. Finally, the role of decision makers as end-users of the methodology and its local adoption is described together with principles for selecting these decision makers. A tool is designed to offer a simple and adaptive way to organize the calculation steps of the risk assessment, making it transferable and effective to use for researchers and practitioners of environmental risk management. Overall, the proposed methodology supports decision-making on drought and heat risks of UGI through systematic risk analysis and risk evaluation.