Transient thermal simulation unusual initial temperature rise and infinite transient state

Hi, as part of a university project I am doing a thermal study on a system that is made to emulate laser absorption.  In order to study this behavior, i have made an assembly with the prototype and did a thermal study (both steady and transient) of this. The one for the steady state seems fine and fits with what we would expect from such a system but the transient one doesn't give the predicted result. First, the system initial temperature is set at 295K, thermal power and convection is set on the solid. The inital temperature is seen to be truly at 295K by putting the time step at very very very small values. The problem is the temperature drastically rises very fast to around 500K in a matter of miliseconds which seems excessif for a total power of around 4 W in the system. Second, if i push the time step to very high value the system actually converges to the expected steady value of temperature but only after around 13000 seconds which doesnt really make sense because the system is supposed to be cooled with fins and 13000 seconds is pretty long. It doesn't change if i crank up the convection coefficient also the time to steady state is the same which is weird. Therefore, i was wondering if someone would happen to know of such problems. I know others in my class have had the same problems but got it fixed they just dont know how. Thank you! 

P.S the assembly to open is named Assemblage pour NG3

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