Since you are talking about this problem appearing with 3 different mini-boxes, and now you say "warm" instead of "hot", I don't believe this is a heat problem, therefore I don't see how the fans would help.
Analog went away a long time ago. That tells me your current splitters are old, and most likely only 1000MHz (or less). Analog also had a stronger signal strength and was more tolerant of deviations.
Splitters don't actually wear out, but they do corrode over time, get full of dust and dirt (and kitchen grease). And the connectors can work loose. Plus, high definition requires more bandwidth.
If your house was wired a long time ago, it may use RG-59 coaxial cable. That was fine back then. And is still fine for short runs. But RG-6 is much better.
I think you should get a pad and pencil and map out your cable network.
Are you using Cox for your Internet too?
I have one 2-way splitter on the coax coming into the house. One side goes to my modem. The other feeds all the TVs in the house. You want to use the minimum number of splits and splitters from there. Note that unused splits still sap signal strength. So, for example, if you have a 3 way splitter going to the bedrooms but only have two mini-boxes feeding off that splitter, the signal strength is still being divided 3 ways even though one split is unused.
I always make my own cables too. This requires a set of "quality" crimpers and some good F-Type coax connectors. Cheap crimpers will cost you more in the long run, and contribute greatly to high blood pressure and hair loss.
The advantage to making your own is if you need a 12 foot cable, you don't have to buy a 25 foot factory made cable.
I would start insisting Cox send a tech out to the house too. They need to measure the signal strength entering your home. If the drop goes back many years that cable should be replaced too. These days they use much better connectors and splitters (if needed) on the outside of the home too.
I had two unfortunate events that ended up being blessings in disguise. The first was a severe storm that came through. I live in
Tornado Alley. This storm took out 1000s of trees and tree branches including a big one that took out my power and cable cables. I had no power for 5 days but that's a different issue. When cox came to restore my cable, they put in a whole new cable, leaving me enough slack inside the house to come directly into my middle bedroom/office closet. This means I have a straight run, no splices or splitters until it gets to this centrally located closet. That's a very good thing.
And right about the same time as that storm, my 30 year-old basement ceiling collapsed. I was furious - until I realized I could see all the floor joists for the main level upstairs. So I wired my house for cable and Ethernet - then put up a new ceiling.
Anyway, my point is, if your cabling is old, and especially uses RG-59, and if planning to stay in that house for a few more years, rewiring may be worth it. At the very least take care of the splitters.