Heroes 3 issues under XP or Vista.

maybe my few words will shed some light on the situation, if you don't mind)

all modern processors are generally x86_64 - that is, they are 64-bit architecture by definition. however, people mostly have operating systems installed for the x86 (32-bit) architecture, although these same processors can quite easily run under an x86_64 OS.
therefore, the user may very well have exactly such a system. and in that case, there really may be problems, because the HoMM3 application is 32-bit.

if I remember correctly, you can find out the type of OS by launching the command line (press win+r -> type cmd there -> press enter), and then run systeminfo there. system information will be displayed, and you should look for a line that says something like "system type: x86-based PC" - this will mean that the system is 32-bit. if it says something like amd64, or x86_64 - then it is a 64-bit system)

and if the OS is indeed 32-bit, then a problem may arise... hmm, I don't even know what to advise)). because Windows is a very "smart" OS, and it doesn't even have any self-diagnosis tools, it practically doesn't write the causes of failures, and I don't think anyone would be interested in digging through the software with a debugger))) usually, if it is not possible to identify the problem by trial and error - as is known - "seven troubles, one solution": reinstallation :D
and there can be many reasons - from a corrupted game distribution, to a hardware conflict - for example, a simple overheating, a faulty driver. although "hardware" problems under Windows are most often accompanied by the legendary BSOD phenomenon, but that is not a certainty. and besides - if some other applications (other games, for example) do not cause similar problems, then everything should be fine with that...
well, in general, see what architecture your OS is - that should make things clearer :)

If the system is x64, then the problem lies in this, Heroes is designed for x86. If there is a multi-core processor, then the problem may be related to the fact that the game interacts incorrectly with the processor. It is recommended to download the CpuControl program, which will distribute processes to cores itself.

wow)) if such software really exists for Windows, then I have no words.... and yes, since HoMM3 is an old game, I don't think it can use more than one core, and perhaps it is not possible to influence this in any way, and it is not really necessary).

p.s. I don't think there is an x64 architecture, right? - as far as I know, 64-bit is usually denoted as either x86_64 or amd64. although I may be wrong.