Then its broken and you should make your landlord fix it.
I don’t think the thermostat is broken.
You can keep filling a bag with air but if the bag has a few holes in it, it’s never going to completely fill up. That doesn’t mean the bag blower is broken, it means the bag is in bad shape.
Yeah, I assume you would have noticed this. Is the furnace constantly on when you set it to 80 and the house temp never goes above 60? If so, the thermostat is most likely not your issue. (I can’t see how it could be the issue, but I don’t like being definitive in cases like this, just in case there’s some edge case I haven’t considered.)
On days when the temperature is normal, I would say 35-80 range, the temperature inside can be regualted comfortably.
But when it’s cold cold, is the furnace constantly working when you set it to 80, or does it shut off?
It shut’s off occasionally but it’s on more than normal than on a plain old cold day. It will just kick off for 30 seconds to a minute.
Based on the rest of what you describe, yes, I think you are in the right to demand the problems get fixed properly. How you can do that depends on the laws in your area. Using Chicago as an example, since these are the laws I know, if the landlord is unresponsive in fixing a problem, the tenant is within their rights to go ahead with fixing it themselves via a professional, deduct the bill from the rent and give the receipt to the landlord. If you have to leave to stay in a hotel, that bill can also be deducted from rent.
Whether you would want to bother with all that at this point, I don’t know, but if you still don’t have hot water, it may be an option if it’s stipulated as a tenant right in your area.
If it’s possible to at least get the code violations reported so the next tenant might have a better chance of things being fixed, that sure would be nice of you, even if you don’t want to pursue it at this point.