I have a dog, who is used to staying at my house while I have gone for work. I leave the door open so that he can go out for hygienic reasons.

During summer, this is not a problem because I stop the heater, and the radiator next to the open door does not lose its warmth.

Now it is becoming more colder, so the radiator next to the open door is losing heat.
Currently, I manage by opening the door (it's a sliding door) just enough for the dog to pass through and along with I am lowering the blinds too but my energy bill is going through the roof.

As you can suggest the easiest solution as shutting my dog out of my house, I think it's too silly to have a guardian dog who can't stop burglars because he can't get into the house to catch them :-)

At this moment the best thing I can think of is a curtain before the door, but I'm curious if somebody can come up with other hacks.

Does anybody have an idea?  

Thanks in advance