Just buy an ultrabook/some laptop with good screen, good network card and long-lasting battery. If heat is the problem for you, I would suggest some aluminum-encased laptop that would disperse heat more easily. IMHO, probably Google chromebook (https://www.google.com/chromebook/) is the kind of device you are looking for...
Also what you need is a remote desktop app. There are quite a few nowadays (from "Remote Desktop" in Windows, to TeamViewer, VNC or etc.). A quite good list is in wikipedia: https://en.wikipedia.org/wiki/Comparison_of_remote_desktop_s... .