The optimization of the battery pack in an off-grid Photovoltaic application must consider the minimum sizing that assures the availability of the system under the worst environmental conditions. Thus, it is necessary to predict the evolution of the state of charge of the battery under incomplete daily charging and discharging processes and fluctuating temperatures over day-night cycles. Much of previous development work has been carried out in order to model the short term evolution of battery variables. Many works focus on the on-line parameter estimation of available charge, using standard or advanced estimators, but they are not focused on the development of a model with predictive capabilities. Moreover, normally stable environmental conditions and standard charge-discharge patterns are considered. As the actual cycle-patterns differ from the manufacturer's tests, batteries fail to perform as expected. This paper proposes a novel methodology to model these issues, with predictive capabilities to estimate the remaining charge in a battery after several solar cycles. A new non-linear state space model is proposed as a basis, and the methodology to feed and train the model is introduced. The new methodology is validated using experimental data, providing only 5% of error at higher temperatures than the nominal one.