I have a Compaq 440BX board running a 500 and has no Northbridge heatsink, it does get warm but not hot. So I say if the board came without one you should be ok as long as you have good airflow thru the case.

Lots of 440BX boards didn't come with a heatsink. I think most of the boards that heatsinked the 440BX were retail enthusiast boards. Whether that was to aid overclocking or just to look good, I don't know.
Many Intel boards that appeared in Dells and such had the chipset bare. But some of those were also heatsinked (I have at least one example on an Intel board), so there is some inconsistency there.

If your CPU cooler has a fan and deflects air onto the chip then that probably mitigates the heat a great deal. But if you don't think it's getting any ventilation then that might be a good reason to be concerned about it.
Given that you don't plan to overclock and that it's probably getting airflow, I think the heatsink would be totally optional.
In theory it could extend the life of the chipset, but these chips weren't failure prone so unless it's working long hours it probably doesn't matter.

Thanks guys. I have pretty good airflow in the case right now, so that isn't a concern. I'll keep using it with the bare chipset for now and later on when I have the chance I may buy a heatsink to put on it.

I have quite a few BX boards and it seems more of a manufacturing (cost?) thing than anything else

With - Asus, Gigabyte, MSI, QDI
Without - Compaq, Dell, Intel

My Tyan tiger 100 dually is in the no column

I have a supermicro 440bx based dual slot 1 board and it has a heatsink on the northbridge

Enthusiast and business solutions may be the ones with a heatsink.