Do you mean, the fan switch on the thermostat? I always have that on On,
rather than Auto. But there isn't a speed adjustment.

What do you mean by "reducing the heat gain"?

blower motor may be adjustable or go to a bigger or faster motor or
larger blower. if the blower is belt driiven often a easy pulley and
belt change is all thats needed. although in the winter too much
airflow can cause drafts.

to reduce heat gain close blinds stuff like that.

do you have air returns from the 3rd floor?