Was googling as couldn't remember the duct.
Turns out I'm missing mine and running my 1Ghz Slot 1 cpu fine

also turns out your not alone
Question about upgrading a Dell Dimension XPS T500 to Socket 370
maybe PM Oeuvre if he doesn't see this?

But would think your fine without the duct as long as the CPU doesn't get that hot and even if it does another strategic fan will probably be enough

is your 1Ghz actively cooled though? I mean is the rear case fan (sans duct) pulling air out, or do you have a CPU fan on the CPU HS ?

To clarify I was asking about running a CPU with a passive heatsink, relying on the duct to pull air out, much like my stock Pentium II 350Mhz that came with the machine (which P3/1Ghz is a far cry from).
If I could get away with it, I was aiming to use a 92mm Noctua that is relatively quiet, and use that for exhaust-duty. Also due to reasons this CPU is capped at 550Mhz anyway (for now..I hope)

yes, stock rear case fan extracting air. The CPU still has the stock heatsink/fan combo though.

I'm not sure I would trust just a passive with your setup. I'd want to increase the airflow over the heatsink. either with a fan mounted on or near the CPU.
running at 550 might be ok though.

Should be fine without it as long as you have the exhaust fan and a fan on the heatsink. I did that for years on my old XPS T550 which I upgraded to a 1GHz Slot 1. I wish I still had that rig.