Hello

Have a look at: Fermi-dirac distribution.

Normal thought is density of states remains unaltered, what changes is the occupation of states, thus Kahled is pointing you in the right direction.

So some bound electrons can go free, and metalic behaviour develops.

Prof. Smrutiranjan Mekap

In addition to the interesting previous answers, you can check the two books by Prof. Rudolf Peierls: Surprises in Theoretical Physics, one of them is the Volume 107 in the series Princeton Series in Physics:

https://doi.org/10.1515/9780691217888

If it instructive to check the plot of the Energy (Y axis) and DoS (x axis), indicating where is located the Fermi energy & how a monovalent metal goes to a semimetal, then to a semiconductor and finally to an insulator with a resulting robust gap and where there finally will be the quantum states located, they can be of different nature, constant or increasing in energy. and the derivative of the number of states with respect to energy gives the DoS.

Then DoS equations can be checked for different insulators models. The dependence on temperature will probably be for the HOMO and LUMO zones. Interesting question at least for me, since I have studied mostly metals in the past.

Kind Regards.

Thank you so much Pedro L. Contreras E.

You are most welcome, Dear Smrutiranjan Mekap

Kind Regards.