Question

when an incandescent light bulb is turned on, its thin wire filament heats up quickly. as the temperature of this wire filament increases, its electrical resistance...

Answer 1

Well, we usually assume that the resistance of a circuit component
is constant and doesn't change.  But the truth is that for anything
that conducts current, its resistance always increases somewhat
when it warms up. 

For things like light bulbs, electric toasters, space heaters, electric
stove burners, the heat coils in a blow-dryer ... anything that's
designed to be really hot when it's doing its job ... the resistance
of those things increases significantly when they come up to their
operating temperatures.