Could these odd apartment mishaps have ordinary explanations?

I’d start by separating the incidents and checking each one on its own. Take a photo of the thermostat and fridge setting, then note the date and whether anyone was cleaning, moving things, or reaching around the controls. A fridge dial can be bumped while loading food, and some controls are easier to turn than they look.

For the painting, check for a nearby vent, a door opening, or vibration from footsteps or appliances. A light frame on a single tack can swing with a small disturbance that’s hard to notice. None of that proves what happened, but it gives you something testable before jumping to a haunting.

The refrigerator is the one I’d deal with first, because food safety matters more than solving the mystery. Use a separate fridge thermometer, and if the food was warm for an unknown length of time, don’t risk eating it. If the dial keeps changing, take a picture of its position and ask the property manager to inspect the control.

Could be boring roommate stuff, even if nobody means to do it. Someone might switch the AC off while adjusting the thermostat, or knock the fridge dial while putting groceries away and not remember afterward. A calm shared note on the controls, plus photos when you leave the room, could show whether there’s a pattern.

For the painting, check the basics: is the tack firmly in the wall, is the frame balanced, and does the motion happen when the heating or cooling system is running? You could hang it with a proper hook and see whether the swinging stops. A loose mounting point makes a lot of movement possible, without needing anything dramatic to explain it.

I wouldn’t treat these events as proof either way. Write down what you observed, what you tested, and what conditions were present, then see whether the same thing can be reproduced. If the apartment has any broader electrical or appliance problems, report those to the landlord rather than focusing only on a paranormal explanation.