HA 0.40.x (0.39.x also) shows errors in termostats temperature graphs. My thermostats are Danfoss 014G0013.

My today's thermostat graph.

That is not limited to the danfoss thermostats. I see something similar with my homematic thermostats. It looks like the most recent value is around time of the last start of home-assistant. The associated temperature sensors of the homematic thermostats do not show this. The eq3btsmart thermostat in another home-assistant installation works as expected.
I see this also with two Ecobee thermostats. Looks like a line is being drawn between the current time/temp and the same temp at the time of restart. Doesn't appear to be happening in the History window, only the climate card.

Unfortunately, the issue has not been fixed in the 0.41 release.
The problem is that the state of the climate component (for the homematic thermostats the operation mode) changes rarely to never. So last_changed keeps constant and the climate graph seems to draw a line from the last last_update time to the last_changed time. Might be fixed by #254
yes, should be fixed by #254
Yep, it's fixed! Just tried in 0.42. Great job, and thanks!
Yes, it's fixed! Great!
Most helpful comment
yes, should be fixed by #254