60 for the CPU isn't that hot. My current one idles around 55C (Core2 Duo E8400 @ 3GHz).
As for your graphic card, it really depends on the maker and model. The latest ATI cards get around 85-90C when in heavy use and they do just fine.
There might indeed be a problem with the engine in that it always draw the full GPU power even when "idle" (although I haven't seen that behavior myself), but if it makes CPU and GPU run dangerously high in temperature, this might show a problem with your PC cooling too. Maybe you can add a specific profile on your graphic card control panel for Demigod and underclock the GPU/CPU slighlty. If you can already run Crysis at high settings, you aren't going to take that much of a hit graphic-wise anyway.
Incorrect.
Actually 60C CPU is bad if its for idle. Under load? Meh a lil high for my standards but with a stock heatsync on the CPU ... i could see it happen. 60C wouldn't be to bad for load.
I have a Quad-Core Q9400 and i idle ~42C and under load ~47-49 (Highest ive ever seen so far = 51C but my PC room was also scorching ... after turnin on my lil window air conditoner it dropped back down to the usual 47-49 under load).
I suggest upgrading your heatsync if your CPU is getting to hot firegoesm0w.
My current heatsync is : http://www.newegg.com/Product/Product.aspx?Item=N82E16835118223 (IF it fits your mobo/processor. Idk what you have so just suggesting something i KNOW is good)
w/ also the thermal paste to ( http://www.newegg.com/Product/Product.aspx?Item=N82E16835100007 ).
What kind of graphic`s card are you using? I have a 8800GT. When Demigod was first released it had the fan on my card running full tilt the whole time. I mentioned this in one of the developer threads. The recent patch`s seem to have improved this. I also tested a large Supcom battle and it didn`t have the card running anywhere near as hot. Demigod had my GT running 100-110C. It is the only game to do this.
I did some looking around and apparently it is not uncommon for the 8 series of cards to get to 115C. A GPU running at 75C should not be a problem. If you`re playing Demigod and you start seeing graphical artifacts and errors, That`s when the card is having problems.
EDIT: I just noticed the OP stated the issue starts at the menu screen, The above only happens in game. These temps all come from a desktop system.
Just because the 8 series cards have been "known" to get to 115C doesn't make that a "good" thing. Ever think about that? 115C = 239F. Thats um ... perty hot for your video card to be. The 8 series has a flaw that not many people have ever realized (but i have) because i have a 8800GTS myself.
The problem with the 8 series is the fan doesn't turn itself up. Plain and simple. The fan on the heatsync of it sits at one speed (mine chose 31% on start) and STAYS there NO MATTER HOW HOT THE CARD GETS. Retarded huh? Would think Nvidia would of caught this ? pfft na of course not!
So many people w/ the 8 series don't know this so 31% fan speed (or somewhere near that) while playing high graphics game = HEAT. To fix this simple little issue (if you have it) DL the program below and follow my guide to fix your overheating issue!
If you have a 8 series card. Below i show you have to set it so your video card won't melt itself!
Note: No pics for some of the first steps (i hope you can figure why i wouldn't do pics of it .. its self-explanitory 
.)
1) DL Rivatuner from here ( http://downloads.guru3d.com/RivaTuner-v2.24-download-163.html ).
2) Install Rivatuner then run it (Note: Rivatuner will build a database thing on first run. It might take awhile depending on system but do not worry it is normal and its ONLY on the FIRST time you run it).
3) After it is open click on the lil arrow you see below.
After installing rivatuner this is what you will see when you first open it.
1)
2) 
Next click on the "System Settings" (The button the looks sorta like a graphics card. 1st one all the way on the left right near the arrow you clicked)
3) 
Next you will see this screen. Click on "Fans"
4) 
In the "Fans" tab you will see something similiar to this screen... at the top right if it is on "auto control" (like above) click and switch to "direct control" and hit "apply" at the bottom right.
5) 
Now it will look like this (once it is on "direct control") Next ...
6) 
Drag the "performance 3d" bar over to about 90% then hit "apply" at the bottom right (you should hear your vid card fan speed up .. its ok its normal and all the other bars should move up to ... rly it doesn't matter which one you move it all controls the same fan LoL).
7) 
Now where it says "Apply fan settings at Windows Startup settings" --- Tick the box (check it) and if the save button lights up after you enable it hit the save button .... then the "apply" at the bottom right and then "ok" and close Rivatuner.
Now your done! 
"Breaking it down" : I am putting this here to break this guide down really fast for what you just did. You installed Rivatuner to turn your video card up for you. Since you saved the settings and set them to start at windows startup ... Everytime your PC boots [i]Rivatuner will AUTOMATICALLY turn your video card fan speed up on boot up so you never have to![i] (As long as you followed this guide correctly).
(Edit for spelling errorz)
Hope this helps. And as always ... http://www.youtube.com/watch?v=z-E8UlrF_9o 
