Numerical analysis of thermal flow, such as computational fluid dynamics (CFD), in industrial product development faces the challenge of rising computational cost for higher accuracy. As an alternative, physics-informed neural networks (PINNs) are gaining attention. However, a significant limitation of PINNs is that they require costly retraining whenever boundary conditions change, such as when object geometry changes. To overcome this, research is advancing the application of graph neural networks (GNNs) to PINNs (PIGNNs). However, existing PIGNNs learn discretized governing equations, which can introduce discretization errors and hinder improvement in accuracy. Therefore, this study proposes a novel PIGNN framework. Specifically, the GNN is first represented as a continuous function using a radial basis function (RBF) network. This approach allows using automatic differentiation to learn the governing equations directly, without discretization. This paper evaluates the effectiveness and challenges of the proposed discretization-free PIGNN compared to conventional discretization-based PIGNN, CFD, and analytic solution in some thermal flow estimation problems.