The end-to-end (E2E) automatic speech recognition (ASR) systems are often required to operate in reverberant conditions, where the long-term sub-band envelopes of the speech are temporally smeared. In this paper, we develop a feature enhancement approach using a neural model operating on sub-band temporal envelopes. The temporal envelopes are modeled using the framework of frequency domain linear prediction (FDLP). The neural enhancement model proposed in this paper performs an envelope gain based enhancement of temporal envelopes. The model architecture consists of a combination of convolutional and long short term memory (LSTM) neural network layers. Further, the envelope dereverberation, feature extraction and acoustic modeling using transformer based E2E ASR can all be jointly optimized for the speech recognition task. The joint optimization ensures that the dereverberation model targets the ASR cost function. We perform E2E speech recognition experiments on the REVERB challenge dataset as well as on the VOiCES dataset. In these experiments, the proposed joint modeling approach yields significant improvements compared to the baseline E2E ASR system (average relative improvements of 21% on the REVERB challenge dataset and about 10% on the VOiCES dataset).