Yes, totally agree THHuxley. I also fell into that rather naive trap of assuming the single time constant. I was surprised it was questioned in the paper when a little thought and searching gave the real and in retrospect obvious reason for the observed change in temperature. Having said that, there is still an issue with slight misalignment in the graph between temperature and power applied.
For me though the most striking observation is that the temperature curve is exactly what you would expect from a heated lump of metal, there is no indication of a abnormal increase indicating the start of some sort of reaction. That would suggest to me there is either no reaction with mismeasurement or a reaction that's proportional in a linear way to temperature. The later would suggest the possibility of a continuous fuel reaction even at room temperature albeit at a very low level.