Arthrospira platensis was cultivated photoautotrophically at 6.0 klux light intensity in 5.0-L open tanks, using a mineral medium containing urea as nitrogen source. Fed-batch experiments were performed at constant flowrate. A central composite factorial design combined to response surface methodology (RSM) was utilized to determine the relationship between the selected response variables (cell concentration after 10 days, X(m), cell productivity, P(X), and nitrogen-to-cell conversion factor, Y(X/N)) and codified values of the independent variables (pH, temperature, T, and urea flowrate, K). By applying the quadratic regression analysis, the equations describing the behaviors of these responses as simultaneous functions of the selected independent variables were determined, and the conditions for X(m) and P(X) optimization were estimated (pH 9.5, T = 29 degrees C, and K = 0.551 mM/day). The experimental data obtained under these conditions (X(m) = 749 mg/L; P(X) = 69.9 mg/L.day) were very close to the estimated ones (X(m) = 721 mg/L; P(X) = 67.1 mg/L.day). Additional cultivations were carried out under the above best conditions of pH control and urea flowrate at variable temperature. Consistently with the results of RSM, the best growth temperature was 29 degrees C. The maximum specific growth rates at different temperatures were used to estimate the thermodynamic parameters of growth (DeltaH* = 59.3 kJ/mol; DeltaS* = -0.147 kJ/mol.K; DeltaG* = 103 kJ/mol) and its thermal inactivation (DeltaH(D) (o) = 72.0 kJ/mol; DeltaS(D) (o) = 0.144 kJ/mol.K; DeltaG(D) (o) = 29.1 kJ/mol).