You indicate that some modifications were made to the piping between the heater and the coke drums, the heater transfer line. If those modifications reduced the velocity in the line, coke could be blocking the line increasing the pressure in the heater. Excessive pressure drop is another reason for a high temperature drop in the transfer line.
I think a normal drum inlet temperature of 468 C (874 F) is too low. Feed temperature can be this low for about an hour before concerns with unconverted oil and tarry drums are high enough to take corrective action. I prefer a normal drum inlet temperature of 482 C to 485 C (900 F to 905 F). A common heater outlet temperature is 496 C (925 F), which should result in an unquenched drum outlet temperature of 440 C (825 F) which is high enough to ensure conversion of the resid in the drum. Higher heater outlets cause faster fouling of the heater, so some trade off in yields vs run time is sometimes done.
As Steve indicated, the primary reason for the drop in temperature in this line is the continued thermal decomposition reactions in the line due to the residence time and the bulk temperature of the fluid. The other reason for a temperature decrease is a reduction in pressure, meaning that equilibrium flash vaporization is occurring in the transfer line using the energy in the liquid to vaporize some of the fluid as the pressure decreases. A typical temperature drop is 14 C (25 F). Your temperature drop before the 18 C, which is similar to the guideline.
If the velocity is too low in the transfer line, coke will form and will not necessarily be uniform in the pipe. Coke that deposits will form stagnant areas that will allow liquid to collect and coke and cause significant back pressure on the heater.
I have not heard of any use of Aerogel insulation on the transfer line. I have seen it used on portions of coke drums and I have heard that it has been used to insulate entire coke drums. I think a mineral wool or calcium silicate insulation would be adequate for the transfer line. Fiberglass is probably an upgrade. I would not put heating coils on the transfer line as that will encourage coke formation in the transfer line.