I measured the C245-036 cartridge with the tip temperature set at 300°C. I used a simple welded ball tip K-Type thermocouple. Ambient temp, 16.7°C as reported by the Fluke. The tip temperature is around 285°C, I added a little bit of solder at the end to help with the heat transfer. The temperature of the cartridge body at the arrow/line near the metal sleeve on the T245 handle is around 80°C. I am not surprise to find the connectors at the end of the cartridge to be at least low 40s°C which is perfectly fine for most plastic.
Like Rufus said the cartridge is built out of thin wall stainless, which explains why, not only it heats up quickly but also sheds heat fast. I have a massive tip C245-407 which I planned to use it on heavy copper such as PC motherboards, I doubt it sheds heat as fast as the smaller tips.