Well, in that case you could have some issues with flesh being burned, too, depending on how hot the heater/register is. Even something that is tolerable for a living hand to touch might cause, ahem, undesirable changes in the deceased over the course of a day. Think of how Egyptian mummies look when unwrapped - they’re well preserved and embalmed, but not exactly how you want Uncle Bob to look at an open casket funeral, ya know?
Up to a point. But only up to a point. Even with professional and timely embalming the average corpse will eventually grow mold on the exterior, for example. Embalming is only good for a couple of days, if a body needs to be held longer it’s usually put in a refrigerator or freezer of some sort.
Someone who, for example, has been fished out of river or decaying in summer time for and extended period is just not going to presentable no matter what you do. Morgues often have something called a “decomp” room (short for “decomposition”) for the really bad cases that even seasoned professionals can find repulsively gross.
Given what you describe, 26 hours still seems a short time, but with the elevated temperature, and depending on cause of death and a few other factors yes, it’s possible the body was in a state where embalming wasn’t going to do much good.