Joint sound event localization and detection (SELD) is an emerging audio signal processing task adding spatial dimensions to acoustic scene analysis and sound event detection. A popular approach to modeling SELD jointly is using convolutional recurrent neural network (CRNN) models, where CNNs learn high-level features from multi-channel audio input and the RNNs learn temporal relationships from these high-level features. However, RNNs have some drawbacks, such as a limited capability to model long temporal dependencies and slow training and inference times due to their sequential processing nature. Recently, a few SELD studies used multi-head self-attention (MHSA), among other innovations in their models. MHSA and the related transformer networks have shown state-of-the-art performance in various domains. While they can model long temporal dependencies, they can also be parallelized efficiently. In this paper, we study in detail the effect of MHSA on the SELD task. Specifically, we examined the effects of replacing the RNN blocks with self-attention layers. We studied the influence of stacking multiple self-attention blocks, using multiple attention heads in each self-attention block, and the effect of position embeddings and layer normalization. Evaluation on the DCASE 2021 SELD (task 3) development data set shows a significant improvement in all employed metrics compared to the baseline CRNN accompanying the task.