Actually No.
If you watch the gauges, when you start an engine, you have max mixture, normally. That helps cool the engine. So, on start up, CHT and EGT are typically low. These temps gradually increase, which is why you want to warm up the engines, before take off. When you are at cruise, you have the mixture leaned out, and that makes the engine more efficient, and raises CHT and EGT.
Hal Stoen has some discussion on this.
http://www.stoenworks.com/Aviation%20home%20page.html
http://www.stoenworks.com/Tutorials/...res%20and.html