<p>Nowadays, many publicly available studies address similar research questions, making meta-analysis an efficient tool for comprehensively synthesizing information from these studies to achieve more reliable model estimation and interpretation. However, conducting a meta-analysis on multiple heterogeneous functional data sets poses significant challenges, particularly when the number of studies is small — a common scenario in this context. In this paper, we propose a novel framework to address this challenge specifically for functional data. The proposed framework is based on the functional fixed-effects model, which extends the classical fixed-effects model to accommodate functional data settings. We also introduce a reparametrization procedure that decomposes the effect function in each study into a common effect function and a deviation function. This approach facilitates the sharing of information across studies while simultaneously accounting for heterogeneity among them. To further enhance information borrowing and reduce noise in model estimation, we propose a region selection procedure to identify null subregions of the common effect function and shrink deviation functions. Simulation studies and real data analysis demonstrate that our framework provides more reliable results and better model interpretation compared to existing meta-analysis methods.</p>