Two issues !
As far as I can see there are two issues to deal with the first is thermal shock this is best avoided by warming the engine at a fast idle speed untill the whole engine has had the chance to walm up to a point at which the rapid diferental expantion of the engine parts will be minimised.
The second issue is lubrication as we all know aircraft piston engine oil technology seems to be frozen in the 1940,s with most of us still using mono grade oils.
These oils do NOT work well untill up to near working temperature and will flow freely between the working parts , this is critical in the highly loaded parts of the engine.
This damage is most commonly seen on the cam lobes and cam followers and is known as "spalling" This is a direct result of lubrication breakdown usualy as a result of the engine being run to fast before the lubrication system has had a chance to build up the "splash lubrication " and the oil is to cold to flow freely.
As the cam and follower spall and small particals of steel are released into the engine , the particals that are not caught in the oil filter normaly embed themselfs in the pistons below the rings and score the barrels this leads to the release of more steel particals flowing around the engine and a rapidly increasing amount of engine damage.
There are two things that can be done to first and most important is to keep the RPM at or below 1200 untill the temp gauge starts to move and then dont do the run-up checks untill you have 40c oil temperature.
The other thing that you can do is use a multi grade oil , these provide better lubrication at low tempertures and some have an anti scuffing agent to help reduce spalling ( this is agent is required for the Lycoming "H" series engines)