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normally when switch on, the transistor operate in triode region. So once ur supply voltage Vgs is bigger, u can get lower Rdson. And try to reduce the body effect also helps to get low Rdson.
The switch resistance is resistance in triode region, i.e 1/K(Vgs-Vt). Here K=uoCox(W/L)
So the switch resistance depends on mobility uo and Threshold voltage Vt. Dependance on temperature is based on temperature dependance of uo and Vt.
Voltage dependance is dependant on variation of Vgs and Vt (body effect). Supply voltage dependance comes when either gate(gate tied to supply) or source voltage depends on the supply voltage.
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