I have a computer with 512 MB, and in the Task Manager I have noticed that this particular game uses this amount of memory and much more during gameplay.
It seems it came with some bug.
If it helps you, I have Windows 2000 SP3, and the Direct X Version wich installs from Heroes 4 CD.
If you won't buy more memory, I recommend you the:
Heroes III Complete, which runs very well with 128 MB, and is
also an excellent and quite addictive game.
Heroes OM&M Forever.