Get a fan for your rats... A/C's today are purposely kept to a smaller range than they used to be as it's more environmentally friendly - uses less electricity to do a reasonable job for what is usually only a couple of months in summer.

I already spent a good chunk on money for a fan for us. Will it really make that much of a difference if the air inside the apartment is above 80 degrees?

Sure, if you have a window open nearby. I can't say how many degrees of difference it will make specifically, but I would also contact some rat expert to find out how serious the 70 degree cut off is and what consequences of 80 F. would be for whatever time periods you anticipate. Rats are usually very tough and survive all over the world in extreme conditions. Your info. might be for ideal conditions, but doesn't mean they'll get sick if summer comes around (are they from the antarctic?).

Get a digital thermometer that can measure both inside and outside temperature. Make sure to get one with a memory feature, which will remember the high and low temperature. Then you can accurately determine if the A/C is cooling the apartment the stated 20 degrees below the outside temperature. Start keeping a daily record of the high temp both inside and outside. "Feels like over 80 degrees" will do nothing to convince a landlord to fix things. You need to prove it.

Ask at the office if they checked your A/C at all, or just left the note.

Check your state regulations for landlords. Are they required to cool their apartments to a certain temperature or to a certain degree below the outside temp? Many states do. If Texas does not, there is probably nothing you can do to make the landlord change the A/C.

If your A/C is working correctly and the apartment is still too hot, can you install your own window A/C to supplement what the landlord provides?

Regards to an air conditioner being able to cool the indoor area no more than 20°F lower than the outdoor temp, that depends entirely on the capacity of the unit.

Air conditioning doesn't so much MAKE cold, as it MOVES heat from one place (inside the house) to another (outside the house). The capacity rating of a unit (such as 12,000 BTU) refers to how much HEAT a unit can MOVE over a stated period of time (one hour). Each 12,000 BTU of capacity is also referred to as a "ton." This comes from 12,000 BTU being roughly the amount of heat required to raise (by adding) or lower (by removing) the temperature of one ton of ice (water at 32°F) by 1°F.

Now, keeping in mind the concept of MOVING heat ... if the unit is too small to overcome the amount of heat that's coming INTO the house (or apartment) by air leakage around doors and windows, radiation through walls and ceilings, etc., along with what's being generated inside by people's bodies, lights and appliances operating and so forth ... then obviously it won't be able to drop the indoor temperature or even maintain a temperature point (the indoor temp will rise as more heat filters in than the unit can remove).

HVAC contractors size units to a "design temperature," which is a specific indoor temperature that the unit can be expected to achieve at a specific outdoor temp, taking into consideration the construction and design of the building (insulation, doors/windows, sun exposure, etc.) ... such as 78°F indoors at 98°F outdoors, which there's your 20°F difference.

There's also the dehumidification factor. Dehumidification is a large part of air conditioning. Dry air feels cooler to the skin (sweat evaporates more readily) than damp air. A unit that's too large won't run enough to dehumidify properly, resulting in a reasonable indoor temperature but a clammy feel. A unit sized just barely large enough to handle the load will run longer (and even continuously when the outdoor "design temp" is reached/passed) and dehumidify better.

Units are sized accordingly such that they work fine the majority of the time, but may fall short when hotter-than-usual weather occurs. Larger-capacity units cost more to buy and more to run, and in these days of conservation concerns and people no longer running their air conditioning at meat-locker temperatures ("design temperatures" are higher than they used to be), smaller-size units are the norm ... except perhaps in the case of public buildings that tend to be overcooled, and homeowners who purposely want their systems larger to better handle weather extremes. Folks living in apartments unfortunately are unlikely to have any say in what the building owners install.

Anyway, the point I'm making is that a blanket statement that "no air conditioner can cool the indoors more than 20°F below whatever is the outdoor temperature" is absolutely wrong.

"Any help would be appreciated with this. I worry for the sake of my rats and do not want the air conditioning to suddenly fail and leave the house above 77 degrees when me and my roommate are away from it."

Your rats are lucky to have such a considerate owner.

If it were me, I'd have a small fan blowing nearby to keep the air moving. I'd also put a shallow dish of water in the cage for them to lay in in the event they become overheated. The air from the fan will make it seem cooler.

Do you use a water bottle? If so, you might want to put a couple of ice cubes in it before you leave for work. That and the dish of water will provide an extra back-up source of moisture in the event that they drink or kick the water out of the dish.

This may be enough to help until you get home. If not, I'd consider asking a friend if you can board them where you know someone will be around in case the power goes out, etc.