Cognitive load (CL) represents the level of demand and difficulty individuals experience during a cognitive task. In this study, we focus on detecting cognitive load using functional near-infrared spectroscopy (fNIRS) due to its non-invasiveness, high spatial resolution, susceptibility to artifacts. We target detailed subject-specific analysis while performing mental arithmetic tasks, and also to identify the time segment at which the CL of a subject is maximum. The work is performed on data from 8 subjects. The experimentation is performed in two modes: window-wise analysis for individual subjects and combined analysis of all subjects. Task and rest periods are segmented into windows of 3 s each. Baseline correction is applied by subtracting the average of the first 6 s. A third-order Butterworth filter with a 0.01–0.1 Hz band-pass eliminated noise from eye movement, Mayer waves, respiration, cardiac activity, and motion artifacts. Z-score normalization is performed for each data split. The preprocessed signals undergoes wavelet transformation using the Mexican hat wavelet, followed by dimensionality reduction with Principal Component Analysis (PCA). The input is then fed to the classifiers such as Support Vector Machine (SVM), 1D Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) at specific time segments (windows) for each subject to detect and analyze CL. An interesting observation is the noticeable variations in performance metrics for each window of each subject in the case of CNN and LSTM. Such variations in the CL across different windows provides valuable insights in determining the temporal load. The experiment is also conducted on the overall dataset with combined subject data, where LSTM shows the highest accuracy (99.14%), followed by CNN (98.89%), and SVM (96.46%) has the lowest accuracy. The overall dataset with all the subjects increases data variability, which is better managed by the adaptive learning mechanisms of CNN and LSTM.