The crystal structure of Sr10Ga6O19 was investigated by in situ single-crystal X-ray diffraction in the temperature range 298-673 K. At ambient conditions the compound shows a (3 + 1)-dimensional modulated structure in the superspace group C2/c(0beta0)s0 [a = 34.9145 (13), b = 7.9369 (2), c = 15.9150 (7) A and beta = 103.551 (3) degrees] with a modulation wavevector of q = 0.4288 (2)b*. Whereas the presented structural model uses first-order harmonic modulation functions only, some features of the modulations are discussed utilizing an electron density derived by the maximum entropy method. Furthermore, two phase transitions were identified: between 453 and 503 K the incommensurate superstructure is replaced by a doubling of the a and b lattice constants, and between 503 and 673 K a phase with the basic cell is formed, identical to alpha-Sr10Ga6O19. Under some cooling conditions crystals showing a combined diffraction pattern of both superstructures can be obtained. The relation of these results to alpha-Sr10Ga6O19 [Kahlenberg (2001). J. Solid State Chem. 160, 421-429] is discussed.