Multi-domain machine translation (MDMT) poses a unique challenge due to varying levels of linguistic complexity across domains. Inspired by human translators' ability to adapt reasoning effort based on difficulty, we propose TwT (Translation with Thought), a resource-rational framework that learns to modulate inference between intuitive and deliberate reasoning. TwT is trained in two stages: (1) supervised fine-tuning on difficulty-aware long chain-of-thought traces distilled from DeepSeek-R1 and rewritten by GPT-4o to reflect human-like reasoning economy, and (2) reinforcement learning with a hybrid reward to optimize translation quality and reasoning efficiency. Evaluated on 15 benchmarks spanning in-domain and out-of-domain settings, as well as 3 seen and 59 unseen languages, with ablations across three backbone models, TwT-7B and TwT-14B outperform much larger SOTA reasoning models in translation quality, while reducing token usage by 32--60\%. These results confirm that aligning translation behavior with cognitive principles enables robust generalization, high translation quality, and efficient reasoning in MDMT.

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