Here is a spreadsheet containing a model of a lumped thermal mass heated by an external (temperature-independent) source as well as an internal (LENR hence temperature-dependent) source. I have rewritten things so that this time you are seeing in the main plot the temperature response of the system to a step input of the external heating. Both the response of LENR and of the nonLENR-equipped reactors are shown.
This time I have used an Arrhenius function to model the temperature dependence of LENR activation. The function, Aexp(-Ea/kT), is parameterized by its activation energy Ea, and the pre-exponential constant, A. T is in degrees Kelvin and k is the Boltzman gas constant (8.62E-5 eV/K/atom). Mizuno, in a 2017 paper empirically found Ea = 0.165 eV/K/atom so that is the value I have used although its value can be adjusted if desired.
The Arrhenius preexponential factor, A, is not speccified in Mizuno's work but I recall that Daniel_G mentioned that the same external power that produced a settling temperature of ~90C for his calibration reactor produced 160C in the active one. I have therefore looked for values of external heating ("Ext") and A that replicate this. Those vlaues are Ext = 75 and A = 5500. There are no units here because I don't know the thermal capacitance of Daniel's reactor, the concentration of the reactants, and so on. Time is therefore best thought of as expressed in heating time constants and power as Joules per time constant.
The time course of the heating curve with the starting parameters shown in the spreadsheet looks exponential but it isn't. It is slower ... particularly as it approaches the final settling temperature. At this point it is instructive to change the value of A to 6500 and see what happens. There is a huge inflection in the heating curve! Temperatures soar to near 4500C which is set by where the Arrhenius function tops out.
Playing with the parameters will build insight. There is much more I can describe and clarify if asked.