Fixed-size learned representations (dense representations, or embeddings) are widely used in many machine learning applications across language, vision or speech modalities. This paper investigates the role of the temperature parameter in contrastive training for text embeddings. We shed light on the impact this parameter has on the intrinsic dimensionality of the embedding spaces obtained, and show that lower intrinsic dimensionality is further correlated with effective compression of embeddings. We still observe a trade-off between absolute performance and effective compression and we propose temperature aggregation methods which reduce embedding size by an order of magnitude with minimal impact on quality.