Although deep networks have been widely adopted, one of their shortcomings has been their blackbox nature. One particularly difficult problem in machine learning is multivariate time series (MVTS) classification. MVTS data arise in many applications and are becoming ever more pervasive due to explosive growth of sensors and IoT devices. Here, we propose a novel network (IETNet) that identifies the important channels in the classification decision for each instance of inference. This feature also enables identification and removal of non-predictive variables which would otherwise lead to overfit and/or inaccurate model. IETNet is an end-to-end network that combines temporal feature extraction, variable selection, and joint variable interaction into a single learning framework. IETNet utilizes an 1D convolutions for temporal features, a novel channel gate layer for variable-class assignment using an attention layer to perform cross channel reasoning and perform classification objective. To gain insight into the learned temporal features and channels, we extract region of interest attention map along both time and channels. The viability of this network is demonstrated through a multivariate time series data from N body simulations and spacecraft sensor data.