This article develops a set of inferential methods for functional factor models that have been extensively used in modelling yield curves. Our setting accommodates both temporal dependence and heteroskedasticity. First, we introduce an estimation approach based on minimizing the least-squares loss function and establish the consistency and asymptotic normality of the estimators. Second, we propose a goodness-of-fit test that allows us to determine whether a specific model fits the data. We derive the asymptotic distribution of the test statistics, and this leads to a significance test. A simulation study establishes the good finite-sample performance of our inferential methods. An application to US and UK yield curves demonstrates the generality of our framework, which can accommodate both sparsely and densely observed yield curves.