I've had issues with very frequent crashes in Windows 7 and what solved it for me was opening the "Windows Task Manager" and finding the "Heroes3.exe" process. Right click on that and select "Set afinity..." There only select 1 of the CPU's and deselect everything else.

That should make the game not crash anymore.

Found this guide that shows it with pictures
http://www.sevenforums.com/tutorials/83632-processor-affinity-set-applications.html

Unfortunately that only applies to that particular instance of the program, it doesn't carry over once you quit. So you'd have to alt-tab out and mess with the process in task manager every single time you run it, which could get annoying.

If you use ImageCFG, it modifies the .exe to only use one processor ever, so you don't have to worry about it any more. There are threads about using ImageCFG and [url=http://www.gog.com/en/forum/heroes_of_might_and_magic_series/stability_issues_heroes_3_on_windows_7/]here.