Amikit 1.3.1 with Winuae 1.4 on a Laptop running WindowsXP. No matter what screen settings I choose in Winuae I get the error message (The selected screen mode can't be displayed in a window, because the desktop is too small for the specified window size. Switching to full-screen mode.) I've tried every display option available with the same results.
If I understood it correctly, your intention is to run AmiKit in a window instead of the full-screen mode. What is the maximum resolution of your laptop? And what resolution do you use inside AmiKit? Here the laptop's resolution is 1280x800 and AmiKit uses the same in full-screen. However such an AmiKit resolution cannot be displayed in a window on Windows desktop because there would be no space for window's borders. Therefore, if your Windows desktop is eg. 1280x800, start AmiKit and set smaller screenmode there using "ScreenMode AmiKit" tool, let's say 1024x768 or even smaller (just don't forget to select the same screenmode using the SYS:Prefs/ScreenMode program as well before you reboot).
If you want to use AmiKit in full-screen and you just want to get rid of the error message, enable "Full-screen RTG modes" option in WinUAE/Display settings.
Clicking OK starts up Amikit normally and the Laptop cooling fan starts and refuses to stop until I either exit out of the emulation or go back to the Windows Desktop. Clicking ctrl F12 goes back to the WindowsXP desktop and the Winuae error message is still there. Nothing I do gets rid of this message short of shutting down Amikit.
Check the CPUIdle slider in WinUAE/CPU settings. It's on the left side by default which means the whole CPU power is dedicated to WinUAE. Move it more to the right to reduce the CPU load. However the emulation will be slower.