I have the same problem,  on ground the TAT is 23C.  I file for FL300 and passing through FL220 I start getting high EGT on all 3 engines.  The only way I can get the EGT to drop is by descending back to FL200.  If I keep climbing or level off at FL220 the EGT goes into the red and will exceed the limits resulting in engine failure.

 

This is not on one flight only.  I thought it was something that I was doing wrong.  But cannot find the problem.  I am using VATSIM Weather on most of my flights.

 

 

I am using VATSIM Weather on most of my flights.

 

This is another part of the high EGT problem. Dont use it. Instead use real or any other weather, provided by your weather engine. Vatsim weather is very buggy, sometimes none at all.