Diffusion Transformer (DiT) faces challenges when generating images with higher resolution compared at training resolution, causing especially structural degradation due to attention dilution. Previous approaches attempt to mitigate this by sharpening attention distributions, but fail to preserve fine-grained semantic details and introduce obvious artifacts. In this work, we analyze the characteristics of DiTs and propose TIDE, a training-free text-to-image (T2I) extrapolation method that enables generation with arbitrary resolution and aspect ratio without additional sampling overhead. We identify the core factor for prompt information loss, and introduce a text anchoring mechanism to correct the imbalance between text and image tokens. To further eliminate artifacts, we design a dynamic temperature control mechanism that leverages the pattern of spectral progression in the diffusion process. Extensive evaluations demonstrate that TIDE delivers high-quality resolution extrapolation capability and integrates seamlessly with existing state-of-the-art methods.