This paper presents an accurate and efficient algorithm for simulating the effects of thermal noise in time-domain. The algorithm presented in this paper is based on Monte Carlo methods and is applicable to linear time invariant circuits. In addition to linear time invariant elements, the algorithm can easily be extended to include clock controlled switches and single or multibit quantizers. This expands the thermal noise analysis capability to switched capacitor circuits and oversampled delta-sigma modulators. Thermal noise generated by different elements is modeled, in the time-domain, by a random pulse waveform having a desired power spectral density. Typically the noise power level is much smaller than that of other desired signals in the circuit and accurate simulation is needed to obtain correct results. In addition, random noise waveforms require the computation of many time points in each transient analysis and efficient simulation methods are needed. In this paper, a new method for computing the transient response of linear time invariant circuits is used. This method accurately and efficiently computes the response to the random pulse waveforms. In addition to thermal noise, the method can also be used to simulate the effect of random dither signals in delta-sigma modulators. Examples of noise simulation are given and, when possible, comparison with measurements, previously published results, or analytical expressions is done.