Hi Rob.
This is sort of explained in the ATM 33.50 section. It was quite challenging to translate and is worth a read because Motronic deals with catalyst temperatures after repeat starts, etc. in quite a clever (but logical) way.
To be fair, I don't think you would have got the answer explicitly, but you might have been able to work it out by reading this module. Some quotes:
"The initial values for the exhaust and catalyst temperature at engine start can be calculated from the temperatures at switch-off and delay times."
"When stopping the engine (C_nachl 0 --> 1) the temperatures tabgm and tkatm are stored.
When starting the engine, the initial temperatures tabgmst and tkatmst are calculated from the switch-off temperature (corrected for ambient temperature) and a factor obtained from maps KFATMABKA or KFATMABKK as a function of tabstatm and tatu."
TTQS
Nope, I mean I see it, but I never would have pulled it from that without being shown. Thank you very much.
Happy/Merry Christmas.
