HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

The slowdown is really due to the rendering, but the processor isn't fully loaded at that moment (one core out of two is loaded at 50%, and the overall load is approximately the same as in windowed mode).

In principle, if you look closely, it seems to lag in windowed mode as well.
But not much,
maybe I'm just too demanding. :)

Okay, maybe this is normal behavior; it's just unusual after 800x600.
Sorry for bothering you.

I can't say for sure, but it might also be due to the video card drivers (you can try downloading the latest version from the manufacturer's website or from wwww.driver.ru). Also, update DirectX.

In DirectX, in the Display tab, is "AGP Texture Acceleration" enabled? If not, then the drivers are definitely not fully functional.

If you have a dual-core processor, there might be a problem with various processes being launched twice, which can cause slowdowns (similar effects). This can be resolved by minimizing and forcibly terminating one of the processes (but you need to identify which one to terminate – usually it's rundll32.exe, which significantly loads the processor).

However, everything runs normally for me, both in DirectX 11 for Win7 (1024x768) and in DirectX 9 for XP (1024x768), both in windowed and fullscreen mode (the resolution is lower than the desktop resolution).

You can also try installing DirectX 10 for XP as an experiment, but the consequences of this are unknown. :) But I don't think it's a big deal to sacrifice one or two Windows installations for the sake of the game:D