I was at Local South Side for a party of 10 people on Friday (Jan 5) at 6PM. There was no heat in the 1st floor of the restaurant despite there being vents and a fireplace (nothing was turned on). The temp on the thermostat was 44 degrees. When we talked to the staff (who were bundled up), they said it is always that cold. My group wore our coats (and gloves!) at the table just to stay warm.
On the positive side, the food wasn't that bad but the temperature caused us to leave earlier than we wanted. Turning on (or fixing) the heat should be a priority - I would not recommend the place without it.