Spiking silicon cochlea sensors encode sound as an asynchronous stream of spikes from different frequency channels. The lack of labeled training datasets for spiking cochleas makes it difficult to train deep neural networks on the outputs of these sensors. This work proposes a self-supervised method called Temporal Network Grafting Algorithm (T-NGA), which grafts a recurrent network pretrained on spectrogram features so that the network works with the cochlea event features. T-NGA training requires only temporally aligned audio spectrograms and event features. Our experiments show that the accuracy of the grafted network was similar to the accuracy of a supervised network trained from scratch on a speech recognition task using events from a software spiking cochlea model. Despite the circuit non-idealities of the spiking silicon cochlea, the grafted network accuracy on the silicon cochlea spike recordings was only about 5% lower than the supervised network accuracy using the N-TIDIGITS18 dataset. T-NGA can train networks to process spiking audio sensor events in the absence of large labeled spike datasets.