Worth 1000, even if it's kindygarten artwork:
The basic point to take from this is that cooltubes which have an air path independent of the airmass in the grow room will remove the vast majority of heat from the lights (upwards of 90%) before it ever comes in contact with the room's airmass.
There's no aircon unit depicted in this (alleged) drawing, but if you find you need it, the only change to make to this arrangement is to run the exhaust blower on a timer so it draws in CO2 laden air for a few minutes an hour. The aircon unit will control the air temp. Without aircon, the exhaust (and intake) blower is run on a thermostat.
A separate blower for the cooltubes is required since the lights must have airflow at all times during lights-on. If you attempt to use the same blower to cool the lights as you use to exhaust the room air (or try to use aircon piped into the cooltubes), you will have no control over air temp, since the blower will have to run constantly- a thermostat can not be used.
The cooltubes don't really care about the temp of the air drawn into them. It would be a bit of a waste to use air from an aircon unit for the lights.