What could lead to engine running hot on climb out?
I'll provide a bit of a general answer to this so it covers for most cases. The basic question is, "my engine is running hot on climb out, what issues could lead to this" 

Cooling Air: Airplane piston engines are air/oil cooled and require proper airflow over the engine to cool properly. A poorly installed cowling or obstructed/damaged air inlets can cause airflow to be incorrect. Some aircraft also have some internal baffling to direct air around the engine bay, these parts can move or get out of place and may be causing improper flow. 

Fuel: As JScarry mentions, you need to ensure you have proper fuel flow (which is key to temp control). If you don't have a flow meter installed a shop should be able to check this for you. 

Procedure: This sounds like a new plane to you, are you following all book procedures for climb out? Turbo planes often have different op-specs than their NA counterparts. Its not uncommon for there to be full power limitations (e.g. full power 5-min continuous limit then reduce to XX MAP).  

Timing: You may have a faulty magneto or your magnetos may be improperly timed causing an advanced ignition situation that would add stress (and heat) to the engine.

Auto-Turbo Settings: I believe the Turbo Toga's had self governing turbos but not all planes do. You should make sure the pop-off mechanism is set correctly and the turbo is operating with in its proper limits. 

Set-Up: This is unique to your new engine case but it may be worth bringing in another A&amp;P that is familiar with the Toga Turbo engine and set up to make sure everything is where it should be just in case the engine shop overlooked something.    

Incorrect Indication: To add to "Set-Up", it's possible that your CHT is incorrectly calibrated or installed. (this is an edit from another poster, who experienced high oil temps to finally discover that the oil temp thermocouple was in the wrong location, and read higher than actual temps)