I don't know what you mean by these power supply connections, labelled case fan only - I've never encountered one.
Fans usually use either a 3 pin motherboard connector, to monitor the speed, or a 4 pin Molex, from the PSU.
You could possibly get adapters, but the only ones I've seen change a fan with a 3 pin to use a Molex connector.
You say things are running hot - how how is hot? Also, what are your other specs?
How are your fans laid out now, and what fans are they?