MOSFET Temperature coefficient
The negative bit at the start is Boltzmann doing his thing on the threshold voltage (Vt). The voltage at which the inversion channel conducts, is lower. At the same time, heat decreases carrier mobility by increasing scattering -- phonons hit them. These effects were mashed together by  Varshni to get an approximately T^2/(a+T) relationship between band gap and temperature. Carrier density is affected by temperature, but it's only significant for temps less than 100K or more than 400K.

Band-gap variation only matters at low Vgs (Vgs &lt; Vt). Once the inversion layer is formed, whatever the band-gap was doesn't matter anymore, as it has been overcome. Carrier mobility effects takes over at higher Vgs.

The image you're showing is for a power FET with Vt=2-4V, so the table shows both effects. Note: Many low Vt FETs have a positive temperature dependence at low voltages (as well as high). I'm not sure what's going on there, but it's something fishy.