I know there is plenty of info out there about care of acoustic guitars in different temperatures/humidity. But I'm looking for help with a specific set of circumstances and wondered if anyone could give me some advice.

I was given an awesome 30-year old acoustic that is in near mint condition. I live in Los Angeles in an older house, so it is not exactly climate-controlled. The indoor temperature in Winter fluctuates from probably 55F at night to 71F during the day. The guitar stays in its case and I tend to only take it out around 8pm when it has been warm for a while. I do have a small space heater that I can potentially leave on low to keep the room warm "enough". I will get a proper humidifying insert for the guitar, once I know which one is the best.

Is this guitar gonna be safe here? In the Summer, the temperature in the house will range more like 65-90F, which I can try to combat a little with the room AC. I'm just wondering how deadly the wide range of daily temperatures is going to be for the instrument if it stays in the case (it's a very good case, not the cardboard kind, more like a flight case)