I think the engine coolant would provide quicker heat to the intake manifold to aide cold performance than utilizing transmission heat (especially on stick shift cars-hah).
On a "cold" Clifforded 250 during the somewhat warm Texas winters, I would tie a newly routed long heater hose (with zipties) along the bottom of the intake to heat more than just the carb base. When spring came, off came the hose-'cause you dont need its help during Texas summers. Nothing ever melted-the truck had a set of Hedmans, not a stock exhaust manifold, hence the need in the first place.