As power density increases exponentially, runtime regulation of operating temperature by dynamic thermal managements becomes necessary. This paper proposes a novel approach to the thermal analysis at chip architecture level for efficient dynamic thermal management. Our new approach is based on the observation that the power consumption of architecture level modules in microprocessors running typical workloads presents strong nature of periodicity. Such a feature can be exploited by fast spectrum analysis in frequency domain for computing steady state response. To obtain the transient temperature changes due to initial condition and constant power inputs, numerically stable moment matching approach is carried out. The total transient responses is the addition of the two simulation results. The resulting fast thermal analysis algorithm leads to at least 10x-100x speedup over traditional integration-based transient analysis with small accuracy loss.