Scene text image super-resolution (STISR) has been regarded as an important pre-processing task for text recognition from low-resolution scene text images. Most recent approaches use the recognizer's feedback as clues to guide super-resolution. However, directly using recognition clue has two problems: 1) Compatibility. It is in the form of probability distribution, has an obvious modal gap with STISR - a pixel-level task; 2) Inaccuracy. it usually contains wrong information, thus will mislead the main task and degrade super-resolution performance. In this paper, we present a novel method C3-STISR that jointly exploits the recognizer's feedback, visual and linguistical information as clues to guide super-resolution. Here, visual clue is from the images of texts predicted by the recognizer, which is informative and more compatible with the STISR task; while linguistical clue is generated by a pre-trained character-level language model, which is able to correct the predicted texts. We design effective extraction and fusion mechanisms for the triple cross-modal clues to generate a comprehensive and unified guidance for super-resolution. Extensive experiments on TextZoom show that C3-STISR outperforms the SOTA methods in fidelity and recognition performance. Code is available in https://github.com/zhaominyiz/C3-STISR.