Most of the engine temps that rise on a hill are cause by the transmission getting hot. Most trans coolers are not big enough.
The reason why the engine temps rise is because the trans fluid goes through the radiator also. This makes the coolant hotter, hence the higher temps..
I installed the biggest trans cooler I could fit. My trans runs 180f as does the truck.
You need a trans temp gauge to know whats happening. If not your guessing.
And IMO if your truck was reaching 230F then your trans is the same or higher. The fluid will turn to varnish and youll be replacing the trans very very soon... ( About $3000 repair for the chevys)
I would change the fluid in the trans ASAP. Get a bigger cooler for the trans, and get a gauge for the trans and take it from there...