Theres no such thing as a stupid question. Nobody on here was born with the knowledge they have now, we all asked the same questions at some point.

What are your stock exhausts like ? If there the normal log manifolds with the snails/horse shoe looking pieces behind them. They work like this.
Cold water comes from the pump and goes in and out of the log section to keep them cool so nobody gets burnt by hot exhaust. Then the water goes through the motor. From the motor all of the water gets dumped into the exhaust (after the snails). They need water all the time so the exhaust heat doesnt melt/burn the hoses that connect to the through transom tips.
With headers, water comes from the pump straight to the motor. From the motor most of the water gets dumped straight overboard through the transom. Only a small amount gets sent to the headers. Water to the headers needs to be controlled in some way (spring loaded T valve, manual valve, electric valve, etc). The idea is to not have water going into the headers at idle when it could be drawn back into the motor through exhaust reversion.
So, both systems will flow the same amount of water through the motor. Yours just dumps all the water out through the exhaust, while a header system dumps most of it out through the transom.
As far as your temp question, most of the time a motor with headers will show a cooler temp than one with logs. Mainly because the logs preheat the water going to the motor a bit.
Hope this helps.