Room acoustical parameters have been widely used to describe sound perception in indoor environments, such as concert halls, conference rooms, etc. Many of them have been standardized and often have a high computational demand. With the increasing presence of deep learning approaches in automatic monitoring systems, wireless acoustic sensor networks (WASNs) offer great potential to facilitate the estimation of such parameters. In this scenario, Convolutional Neural Networks (CNNs) offer significant reductions in the computational requirements for in-node parameter predictions, enabling the so-called Artificial Intelligence-Internet of Things (AI-IoT). In this paper, we describe the design and analysis of a CNN trained to predict simultaneously a set of common room acoustical parameters directly from speech signals, without the need for specific impulse response measurements. The results show that the proposed CNN-based prediction of room acoustical parameters and speech intelligibility achieves a relative error rate of less than a 5.5%, accompanied by a computational speedup factor close to 250 with respect to the conventional signal processing approach.