Heat stress (HS) negatively affects dry matter intake (DMI), milk yield (MY), feed efficiency (FE), and free water intake (FWI) in dairy cows, with detrimental consequences to animal welfare, health, and profitability of dairy farms. Absolute enteric methane (CH4) emission, yield (CH4/DMI), and intensity (CH4/MY) may also be affected. Therefore, the goal of this study was to model the changes in dairy cow productivity, water intake, and absolute CH4 emissions, yield, and intensity with the progression (days of exposure) of a cyclical HS period in lactating dairy cows. Heat stress was induced by increasing the average temperature by 15°C (from 19°C in the thermoneutral period to 34°C) while keeping relative humidity constant at 20% (temperature-humidity index peaks of approximately 83) in climate-controlled chambers for up to 20 d. A database composed of individual records (n = 1,675) of DMI and MY from 82 heat-stressed lactating dairy cows housed in environmental chambers from 6 studies was used. Free water intake was also estimated based on DMI, dry matter, crude protein, sodium, and potassium content of the diets, and ambient temperature. Absolute CH4 emissions was estimated based on DMI, fatty acids, and dietary digestible neutral detergent fiber content of the diets. Generalized additive mixed-effects models were used to describe the relationships of DMI, MY, FE, and absolute CH4 emissions, yield, and intensity with HS. Dry matter intake and absolute CH4 emissions and yield reduced with the progression of HS up to 9 d, when it started to increase again up to 20 d. Milk yield and FE reduced with the progression of HS up to 20 d. Free water intake (kg/d) decreased during the exposure to HS mainly because of a reduction in DMI; however, when expressed in kg/kg of DMI it increased modestly. Methane intensity also reduced initially up to d 5 during HS exposure but then started to increase again following the DMI and MY pattern up to d 20. However, the reductions in CH4 emissions (absolute, yield, and intensity) occurred at the expense of decreases in DMI, MY, and FE, which are not desirable. This study provides quantitative predictions of the changes in animal performance (DMI, MY, FE, FWI) and CH4 emissions (absolute, yield, and intensity) with the progression of HS in lactating dairy cows. The models developed in this study could be used as a tool to help dairy nutritionists to decide when and how to adopt strategies to mitigate the negative effects of HS on animal health and performance and related environmental costs. Thus, more precise and accurate on-farm management decisions could be taken with the use of these models. However, application of the developed models outside of the ranges of temperature-humidity index and period of HS exposure included in this study is not recommended. Also, validation of predictive capacity of the models to predict CH4 emissions and FWI using data from in vivo studies where these variables are measured in heat-stressed lactating dairy cows is required before these models can be used.