I live in an apt as well. I just turn on the ac before I leave for work if I know it's getting above 80's. It has worked fine for me. As others have said you'll want a box fan to blow cool air into said room.
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I have the same setup it seems as you do. AC in the living room with the two bedrooms with no AC. To put it bluntly this setup sucks when attempting to cool off the back rooms. If the door is closed to either bedroom they roast in the summer. I usually have to use large box fans to move the air around to make the back rooms tolerable... PITA but cheap rent...
The window tint is a good idea. Just an FYI you can get the stuff at WalMart that is static cling to the window so it isn't a permanent installation and can be taken down at anytime with no issues... I have never used the screen but that may work just as well.
The portable AC units that are on wheels do work pretty well. It doesn't take a large one to cool the room that size. Most of them come with an attachment to vent the hot air to the outside. It might be more productive for you (or at least have the dual benefit of a cooler apt and cooler tank) to go with the AC unit over a cooler. From what I have seen they are about the same cost but with the AC unit you can cool off the whole apartment better so you benefit along with your tank.
Also think about adding a high humidity level to the already high temps...
What floor of said apt are you on? 140 Gal is a lot of weight for some apts.
The AC should help with the humidity as well. Probably a better bet than a chiller for you. It is nice if the "viewing room" is comfortable and not like a jungle in July.