Time Series Foundation Models (TSFMs) have shown promising generalization capabilities across diverse domains, but their adaptation in data-scarce environments remains a critical challenge. This thesis explores whether fine-tuning on a related, data-rich subdomain improves performance in a low-resource target subdomain. A two-stage fine-tuning framework is introduced: first, adapting a pre-trained TSFM to a data-rich source domain; then, progressively fine-tuning it on the target domain as new data becomes incrementally available. Three strategies for incremental fine-tuning are evaluated: Progressive Incremental Fine-Tuning, Independent Incremental Fine-Tuning, and Independent Full Fine-Tuning. Experiments were conducted across three domain pairs, Greek and Italian electricity load, Bitcoin and Ethereum prices, and Athens and Izmir temperature records, using MAPE and MWQL as evaluation metrics. The results show that the effectiveness of progressive finetuning is highly domain-dependent. In the cryptocurrency and weather temperature domains, the proposed method yielded significant performance improvements, with an average uplift of approximately 7.6% in MWQL for cryptocurrency and 11.5% for weather data. This suggests that knowledge transfer is highly effective when the source and target domains (e.g., Bitcoin/Ethereum prices or Athens/Izmir temperatures) share strong statistical similarities. Conversely, in the electricity load domain, this approach resulted in a notable performance degradation of about 30% in MWQL compared to the baseline. This highlights the challenges of knowledge transfer between domains with disparate data distributions, such as the distinct energy consumption patterns of Greece and Italy. The findings underscore both the potential and the limitations of progressive fine-tuning, demonstrating that while it can accelerate adaptation in similar domains, its success is not guaranteed and depends critically on the degree of domain similarity