So a few things here. I’m using a global temp table instead of a local one because it makes it easier to reference. Local temp tables aren’t listed in tempdb under their name while global ones are.
The first part of this message (the bit in black) is a warning basically telling us that if there is a temp table (a # at the front of the name) it’s going to ignore the multi part reference. In other words, you’re going to get this message any time you try to use a multi part name and a temp table. Linked server or not. The second part of the message (the bit in red) just tells us that there isn’t a temp table named ##DBList.
Kenneth finds a way, but I can’t think of a scenario where accessing a temp table on a different instance turned out to be a good idea.