On the Role of Temperature Sampling in Test-Time Scaling

TL;DR

This paper shows that simply increasing the number of samples $K$ in test-time scaling yields diminishing returns for LLM reasoning. It introduces temperature scaling as a complementary axis of scaling, revealing that different temperatures solve different hard problems and that a multi-temperature strategy expands the model's reasoning boundary beyond any single temperature. Through entropy analyses and case studies, it characterizes why temperature diversity unlocks latent capabilities and proposes a multi-temperature voting method to exit easy questions early, achieving substantial efficiency gains. The findings demonstrate that base models, when scaled across temperatures, can match RL-trained performance on several benchmarks, offering a simple, practical route to enhanced reasoning without additional training.

Abstract

Large language models (LLMs) can improve reasoning at inference time through test-time scaling (TTS), where multiple reasoning traces are generated and the best one is selected. Prior work shows that increasing the number of samples K steadily improves accuracy. In this paper, we demonstrate that this trend does not hold indefinitely: at large K, further scaling yields no gains, and certain hard questions remain unsolved regardless of the number of traces. Interestingly, we find that different sampling temperatures solve different subsets of problems, implying that single-temperature scaling explores only part of a model's potential. We therefore propose scaling along the temperature dimension, which enlarges the reasoning boundary of LLMs. Averaged over Qwen3 (0.6B, 1.7B, 4B, 8B) and five representative reasoning benchmarks (AIME 2024/2025, MATH500, LiveCodeBench, Hi-ToM), temperature scaling yields an additional 7.3 points over single-temperature TTS. Temperature scaling also enables base models to reach performance comparable to reinforcement learning (RL)-trained counterparts, without additional post-training. We further provide a comprehensive analysis of this phenomenon and design a multi-temperature voting method that reduces the overhead of temperature scaling. Overall, our findings suggest that TTS is more powerful than previously thought, and that temperature scaling offers a simple and effective way to unlock the latent potential of base models.

Figures (10)

• Figure 1: Observations and motivation for temperature scaling in TTS. (a) RL vs. TTS: RL produces long single traces, while TTS generates multiple shorter ones. (b) Pass@$K$ and $-\log(\text{Pass@}K)$ curves at $T=0.7$ on Qwen3-4B (AIME 2025); no gain beyond $K=1{,}024$. (c) Question solvability on AIME 2025 for Qwen3-4B: different temperatures solve different subsets of questions. (d) Single-temperature vs. multi-temperature scaling: the latter expands the reasoning boundary.
• Figure 2: Scaling temperature for test-time compute on Qwen3-4B. (a) Pass@$K$ curves for different temperatures on AIME 2025 Q22. (b) Distribution of preferred temperatures across AIME 2024/2025. (c) Pass@$K$ scaling curves on AIME 2025. (d) Avg@$1,024$ curves across five datasets.
• Figure 3: Comparison of scaling along $K$ and scaling along $T$. (a) Correlation of Avg@$1,024$ across two temperatures on AIME2025, Qwen3-4B. (b) Correlation of Avg@$1,024$ across two temperatures on AIME2025, Qwen3-8B. (c) Scaling $K$ vs. scaling $T$ on AIME2025, Qwen3-4B. (d) Temperature scaling vs. RL-trained model on AIME2025, Qwen3-4B, thinking mode.
• Figure 4: Entropy dynamics of Qwen3-4B across temperatures on AIME 2025. (a) Q16. (b) Q29. (c) Q11. (d) Across the whole dataset.
• Figure 5: Entropy distributions and temperature subset. (a) An easy problem (AIME 2025 Q16, Qwen3-4B). (b) A hard problem (AIME 2025 Q25, Qwen3-4B). (c) Temperature minimal subset for Qwen3-4B.