A major experimental problem in many isoperibolic calorimetric studies is the fact that the decrease in the electrolyte level due to electrolysis produces a significant decrease in the apparent calorimetric cell constant if the temperature is measured in the electrolyte of the electrochemical cell. Furthermore, heat transport pathways out of the top of the cell can produce large errors, especially at low power levels. There is no steady state in electrochemical calorimetry, so accurate results require the evaluation of all terms in the differential equation governing the calorimeter; These factors have contributed to the controversy involving measurements of excess power during Pd-D2O + LiOD electrolysis experiments. A critical analysis is presented for several key publications that have impacted this scientific topic.