This paper proposes a mathematical model for online prediction of the hematocrit- and temperature-based normal blood viscosity during cardiopulmonary bypass (CPB). Clinical trials were performed using a previously developed continuous blood viscosity monitoring system, and continuous pressure- and flow-based instantaneous viscosity (eta(e)) data were collected from 40 patients subjected to mild to moderate hypothermic CPB. The hematocrit and blood temperature data corresponding to (eta(e)) were also acquired. It was found that the blood viscosity-temperature curves for the different hematocrit levels can be well fitted using linear models, with the parameters of the linear model (slopes and intersects) also exhibiting linear relationships with the hematocrit. Based on these relationships, we were able to predict the hematocrit- and temperature-based normal viscosity (eta(e)). To test the prediction accuracy, (eta(0)) was compared with (eta(e)) using the leave-one-out cross-validation procedure. Furthermore, eta(0) and the offline-measured viscosity (eta), determined using a conventional viscometer, were compared for 20 patients subjected to mildly hypothermic CPB. eta(0)-eta(e) two online blood viscosity monitoring methods based on different principles-showed good agreement (R-2 = 0.74 and p < 0.0001). The proposed model is suitable for online prediction of the hematocrit- and temperature-based normal blood viscosity during CPB. The proposed model can function as the core of a future application for investigating the effects of blood viscosity during clinical perfusion management and facilitate detailed online blood viscosity studies.