Using thermal gravimetric analysis, we recently showed that there is a temperature dependent phase transition in Li1+xMn2-xO4 which involves oxygen loss. The temperature of the phase transition, T-cl, depends linearly on x over the range from x = 0 to x = 0.20. Here we discuss the origin of the phase transition and show that it is caused by the disproportionation of Li1+xMn2-xO4 into Li2MnO3, oxygen, and Li1+xMn2-xO4 where x’ < x. X-ray diffraction measurements of samples quenched from above T-cl show that this produces Li2MnO3. Furthermore, the weight loss of the samples above T-cl can be accounted for by a simple model which describes the disproportionation reaction. Calculations of the rate change of sample mass with temperature, dM/dT, agree well with the measured data. A phase diagram for the maximum attainable x in Li1+xMn2-xO4 is presented as a function of temperature for samples heated in air. These results show that the optimum method for preparing materials with low specific surface area and large values of x is a two-step method. The first step involves heating materials with x about equal to zero to about 850 to 900 degrees C to lower the surface area, and the second involves reacting this intermediate with additional lithium salt near 600 degrees C, which avoids Li2MnO3 formation. Such materials with x near 0.15 show excellent capacity retention vs. cycle number in secondary lithium coin cells even at 55 degrees C.