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In a certain nanoparticle that behaves like the Einstein model, one quantum of energy equals $1\mathrm{.}7{10}^{-23}J,$ which is the smallest amount of energy that can be added to the nanoparticle. When the internal energy of the nanoparticle is equal to $2000$ quanta, there are $7\mathrm{.}539{10}^{64}$ ways to arrange these $2000$ quanta of energy in the nanoparticle. If one more quantum of energy is added to the nanoparticle, the number of ways to arrange the $2001$ quanta of energy increases to $7\mathrm{.}649{10}^{64}.$ What is the absolute temperature of this nanoparticle? Recall that $k_B=1\mathrm{.}38{10}^{-23}\frac{J}{K}.$

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