nmos used as switches for resistance trimming in bgr circuits cause large output voltage variations with temperature. Such variations would not be there if the trimming circuit is not included. May I please have suggestions.

BG voltage is the addition of a Vbe forward biased junction (negative tempco) and a PTAT voltage (positive tempco). The optimal value has zero first order temperature dependence (but there are a lot of secondary effects like the resistor values vs temperature). what is the dependence you say caused by the trim circuitry? do you see effects even with all switches open? if this the case the transistors have some leakage.