The success of contrastive learning models like CLIP, known for aligning 2D image-text pairs, has inspired the development of triplet alignment for Large 3D Point Cloud Models (3D-PCM). Examples like ULIP integrate images, text, and point clouds into a unified semantic space. However, despite showing impressive zero-shot capabilities, frozen 3D-PCM still falls short compared to fine-tuned methods, especially when downstream 3D datasets are significantly different from upstream data. Addressing this, we propose a Data-Efficient, Training-Free 3D Adaptation method named PointTFA that adjusts ULIP outputs with representative samples. PointTFA comprises the Representative Memory Cache (RMC) for selecting a representative support set, Cloud Query Refactor (CQR) for reconstructing a query cloud using the support set, and Training-Free 3D Adapter (3D-TFA) for inferring query categories from the support set. A key advantage of PointTFA is that it introduces no extra training parameters, yet outperforms vanilla frozen ULIP, closely approaching few-shot fine-tuning training methods in downstream cloud classification tasks like ModelNet10 & 40 and ScanObjectNN. The code is available at: https://github.com/CaoChong-git/PointTFA.