Textbooks on heat transfer generally refer to Newton's law of cooling but they give no details of Newton's experiment. The purpose of the first part of this paper is to give details of Newton's work. His explanation of why he thought the law was correct, and the experiment that he did to confirm it, are still of interest. It is worth stressing that he did not write his law down in the form of an equation nor did he define or use the heat transfer coefficient. He was however the first to postulate that the rate of loss of temperature of a hot object, with air blowing past, is proportional to the temperature itself. The second part of the paper is an attempt to reconstruct Newton's transient cooling experiment using modern knowledge of heat transfer. It is necessary to allow for varying heat transfer coefficients and specific heats and hence a numerical approach has to be used on a computer. The output of the process is data for temperature versus time for the test section. The next step is to take this simulated cooling time data and analyse it using the same method Newton used, to produce the same type of estimated temperatures that he obtained. By modern standards his estimates of the melting point of various metals were too low. It has been suggested that this was because the metals were impure but a purely heat transfer explanation is shown to be more plausible. A simple extension of his explanation of why the law works is used to derive a result close to accepted modern equations for heat transfer coefficient.