Actual evapotranspiration (ET_a) plays a crucial role in the water and energy cycles of the earth. An accurate estimate of the ET_a is essential for management of the water resources, agriculture, and irrigation, as well as research on atmospheric variations. Despite the importance of accurate ET_a values, estimating and mapping them remains challenging due to the physical and biological complexity of the ET process. As a novel approach for rapid and reliable estimation of ET_a, the present study develops automated deep learning (AutoDL) models that incorporate a metaheuristic optimization algorithm for image processing, architectural design, and hyperparameter tuning. The proposed AutoDL models integrate three different spatial and channel attention mechanisms, including a novel activated spatial attention mechanism (ASPAM), with the U-Net architecture. Bypassing the need for meteorological inputs, the proposed framework uses Moderate Resolution Imaging Spectrometer (MODIS) products and Digital Elevation Model (DEM) data as inputs. To evaluate the performance of the models, they are applied to three study areas in the United States with various climatic characteristics. According to the results, during the spring and summer, when the target values have higher certainty, the estimations are highly promising, with R² as high as 0.91 and MAPE as low as 6.40%. Furthermore, the proposed ASPAM module improves the accuracy of ET_a estimations compared to attention gate (AG) and squeeze and excitation (SE) attention modules. The results also indicate that the MODIS raw products and derived vegetation and water indices can predict ET_a within a reliable range of accuracy, with the addition of DEM data marginally enhancing the models' performance. The automatic workflow of this model makes it significantly easy to use, contributing to its applicability and generalizability for enhancing atmospheric research.