I never trust the image I see on the camera LCD for judging exposure or colours, as it isn't all that accurate. It is really only there so you can see if you got the shot or not.
Also you have to understand the difference between what you see on the camera and what you see in a raw editor, they are two different files and can look very different. The raw image on your computer is just that, raw data converted to an image by the software on the computer to a set of default values that you have chosen (or not, if that is the case, but it still has default values). The image on your LCD is a jpeg that has been processed, often significantly, and will display those changes. If you are not using a picture style that is quite minimal in what it does (such as faithful or neutral) then the processing could be cranking up the contrast and saturation, changing the colour balance (landscape for instance punches up the greens, portrait attempts to get the best flesh tones) and more. If you have some fairly heavy mods going on in picture styles, they will ONLY affect the jpeg and that is what is used on the camera LCD. The original (unpunched) raw could look very subdued by comparison, but you will only see that on your computer.
I can remember when I first started using raw I got quite disheartened when opening files in PS, they initially opened all bright and punchy then after a few seconds went comparatively drab and lifeless (until I processed them). This was because PS first opened the jpeg preview file while it rendered the raw file, then switched to the raw.
Some camera LCDs do have a slight colour cast as well (my original 5D has a quite noticeable one) and that could explain why one image is warmer on the camera than on the computer. You are looking at different files, processed differently, on different hardware, which may not be calibrated identically. I would be very surprised if they looked identical.