Not a bad summary Oldbones.
In fact I like it, good job here!!
TEM: Terrain Effects Modifier.
As you know terrain will effect combat and the effect will include the terrain the defender is sitting in along with hex side terrain that crosses the line of sight/line of fire where the attack is coming from. Examples of hex side terrain would be low walls, hedges etc. Example of in hex terrain would be woods, village, industrial, orchard etc.
For direct fire attacks hex side TEM comes into play. For indirect fire attacks it doesn't.
For direct and indirect fire attacks in hex TEM comes into play.
I think around page 53 of the manual explains how combat is calculated and how TEM effects that calculation.
In the meantime if you have any other questions about the game, there is a number of game veterans around here like me who would be happy to help!
Thanks
Ivan the Big