Absolutely without doubt leave the door open. Some will say it matters whether split system in sunroom is heat pump,nat gas or resistance heat. Others will get hung up on insulation, windows and such. Don't sweat the small stuff, recent research says it simply doesn't matter.

I have a tiny greenhouse on the back of my house, and it gets up to 120 degrees on a sunny winter day, so we will,open up the slider. But I have to remember the slider is open if you leave the house or it clouds over since the temperature plummets quickly.

The principles of heat transfer by convection have been well established for more than a century. A 2F temperature differential is a pretty small driving force for heat transfer. Without air being mechanically supplied to the sunroom (as it would be with a forced air heating system,) I wouldn't expect much mixing. That said, the amount of outdoor air infiltration the systems need to deal with can be affected by opening up the door between the two spaces.

@klem1, please cite your source(s) for "recent research" on this topic. Inquiring minds want to know....

A lot depends on weather and time of day/night.