Talking Face Generation (TFG) strives to create realistic and emotionally expressive digital faces. While previous TFG works have mastered the creation of naturalistic facial movements, they typically express a fixed target emotion in synthetic videos and lack the ability to exhibit continuously changing and natural expressions like humans do when conveying information. To synthesize realistic videos, we propose a novel task called Emotionally Continuous Talking Face Generation (EC-TFG), which takes a text segment and an emotion description with varying emotions as driving data, aiming to generate a video where the person speaks the text while reflecting the emotional changes within the description. Alongside this, we introduce a customized model, i.e., Temporal-Intensive Emotion Modulated Talking Face Generation (TIE-TFG), which innovatively manages dynamic emotional variations by employing Temporal-Intensive Emotion Fluctuation Modeling, allowing it to provide emotion variation sequences corresponding to the input text to drive continuous facial expression changes in synthesized videos. Extensive evaluations demonstrate our method's exceptional ability to produce smooth emotion transitions and uphold high-quality visuals and motion authenticity across diverse emotional states.