Experiments for studying the effects of climatic change on ecosystems often involve manipulation of one or several quantitative treatment factors of interest. Response surface regression is the method of choice for these types of experiment. Here, we describe the development of a design of a free air CO2 enrichment experiment with two quantitative treatment factors, that is, elevated temperature and CO 2 enrichment. The design strategy takes account of budget constraints imposing limitations on the number of plots with elevated temperature and CO 2 levels. The approach is based on polynomial regression models and is focussed on an efficient estimation of interaction between the two treatment factors. Extension to more than two factors is straightforward. An analysis of soil moisture data demonstrates the overall suitability of the proposed design to analyse non‐linear interactions of two (or more) global change factors.