Given a stream of Twitter messages about an event, we investigate the predictive power of features generated from words and temporal expressions in the messages to estimate the time to event (TTE). From labeled training data average TTE values of the predictive features are learned, so that when they occur in an event-related tweet the TTE estimate can be provided for that tweet. We utilize temporal logic rules and a historical context integration function to improve the TTE estimation precision. In experiments on football matches and music concerts we show that the estimates of the method are off by 4 and 10 h in terms of mean absolute error on average, respectively. We find that the type and size of the event affect the estimation quality. An out-of-domain test on music concerts shows that models and hyperparameters trained and optimized on football matches can be used to estimate the remaining time to concerts. Moreover, mixing in concert events in training improves the precision of the average football event estimate.