Fiber Specklegram Sensors (FSS) are vital for environmental monitoring due to their high temperature sensitivity, but their complex data poses challenges for predictive models. This study introduces Prion-ViT, a prion-inspired Vision Transformer model, inspired by biological prion memory mechanisms, to improve long-term dependency modeling and temperature prediction accuracy using FSS data. Prion-ViT leverages a persistent memory state to retain and propagate key features across layers, reducing mean absolute error (MAE) to 0.71$^\circ$C and outperforming models like ResNet, Inception Net V2, and Standard Vision Transformers. This paper also discusses Explainable AI (XAI) techniques, providing a perspective on specklegrams through attention and saliency maps, which highlight key regions contributing to predictions