Have you tried the other ODE-integrating functions? From your problem description it sounds like your ODEs are stiff - for that ode23 is not the optimal function, perhaps you get much better success with ode15s or oed23s that both are designed for stiff ODEs. One further note is that to me it seems like the temperature-derivative does not depend on the other 2 parameters, perhaps you can refactor the problem to first integrate that ODE and then use that solution when integrating the other 2.
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