My experience is with direct fired heaters. I would suggest you find seek out the papers by Lobo and Evans in addition to the work of Hottel to understand more.
1. crossover temperature - this is temperature of the fluid being heated at the point exiting the convection section/entering the radiant section.
2. cold plate area tube wall - I've always seen this referred to as cold plane area. It depends on the radiant tube surface area and how the tubes are laid out. Generally though, it is equal to (exposed tube length)x(center-to-center spacing)x(number of tubes exclusive of the shield tubes)
3. cold plate area shield tube - Same as above but for the shield tubes. The lowest 1 to 3 rows (depending on who you talk to) of the convection section are called the shield (or shock) tubes. Beyond the 3rd row , there is not appreciable radiation from the radiant section.
4. mean beam length - A factor that seeks to account for the effect of the geometric layout on the radiation of a gas volume to its boundary. There are tables available with equations to calculate MBL for typical heater layouts.