CFM56 engine icing in the climb?
 

Will the CFM56 ice up at full thrust in the climb?

A few years ago we were given this condition in a B737-300 SIM check. We didn't carry out the QRH icing drill accurately enough with respect to timing at different thrust settings and the instructor failed the engine to make a point . . .

I am aware that the CFM56 will ice up nicely at medium levels. BUT severe icing at full thrust climbing is something I have never heard of.

Anybody experienced this conditon and care to comment?