I have had the worst time getting my Nest Gen 3 T stat to work with my dual duel system. Heat pump with propane gas. the A/C works fine, but when the outside temp goes below the set point (38 F) usually the furnace does not turn On. The most frustrating part is there is no help. One is left to their own resources to figure it out. No help line or chat, nothing. Google has really dropped the ball on this one.
I'm sorry for the trouble this may have caused you — let's see what's going on.
I did find a helpful article with some troubleshooting steps for lockout or breakpoint temperatures. Please let me know if that helps or if the issue still persists.