The answer is: exactly like any other titration, except that the heat of the reaction between the analyte and the titrant is used to detect the endpoint. Let's take an example: you want to determine the sulfate content of a particular sample. Your titrant will be 1 mol/L barium chloride. The reaction of barium ions with sulfate ions to form insoluble barium sulfate is exothermic (heat is given out by the reaction). In a thermometric titration, the burette delivers titrant at a constant dose rate, so the reaction between the barium and sulfate ions is occurring at a constant rate. In an exothermic reaction, you'd expect that the temperature would increase at a constant rate too. There are a few other things around like heats of mixing and stuff, but by and large, we see an increase in temperature. Check the titration plot from a Metrohm 859 Titrotherm instrument below. The red line is the temperature trace of the reaction. The volume of titrant added is plotted on the "x"-axis, the solution temperature is plotted on the "y"-axis. When all the sulfate has reacted, there is nothing to increase the solution temperature at the same rate, and we see a break in the curve. That's the "endpoint" or "breakpoint" of the titration. We measure the amount of titrant added to this point, and calculate the equivalent amount of sulfate that this represents.
Finding the exact endpoint used to be a tedious business until cheap PC's came along to run the powerful algorithms needed to get accurate results. In thermometric titration, the second derivative of the temperature plot is used to locate the endpoint, as you can see in the next titration plot.
The yellow curve represents the second derivative. The endpoint is at the peak shown on this curve. Of course, there's some pretty flash maths going on the background, but you and I don't have to worry about that. The results can be sent automatically to a dedicated spreadsheet for calulation, which all makes it pretty easy.
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