Power densities in modern processors induce thermal issues that limit performance. Power and thermal models add complexity to architectural simulators, limiting the depth of analysis. Prohibitive execution time overheads may be circumvented using sampling techniques. While these approaches work well when characterizing processor performance, they introduce new challenges when applied to the thermal domain. This paper aims to improve the accuracy and performance of sampled thermal simulation at the architectural level. To the best of our knowledge, this paper is the first to evaluate the impact of statistical sampling on thermal metrics through direct temperature measurements performed at runtime. Experiments confirm that sampling can accurately estimate certain thermal metrics. However, extra consideration needs to be taken into account to preserve the accuracy of temperature estimation in a sampled simulation. Mainly because, on average, thermal phases are much longer than performance phases. Based on these insights, we introduce a framework that extends statistical sampling techniques, used at the performance and power stages, to the thermal domain. The resulting technique yields an integrated performance, power, and temperature simulator that maintains accuracy, while reducing simulation time by orders of magnitude. In particular, this paper shows how dynamic frequency and voltage adaptations can be evaluated in a statistically sampled simulation. We conclude by showing how the increased simulation speed benefits architects in the exploration of the design space.