Man I cant believe what I am reading here. First off, no way a stopped up AIR cleaner would make an engine run hot. If it cant get air, it is going to run rich and rich means cooler. Stopped up radiator from grass seeds, YEP.
When working in dusty conditions like mowing fields or working dirt, the air cleaner should be cleaned daily.
Black filter paper is not a reason to throw away a filter. Check the filter by shining a flash light on it and viewing the opposite side. You can see if it has holes or if it is stopped up. They are made to be cleaned with compressed air, just dont put the tip right against it. The filter is going to be the color of your dirt, if your dust is brown or black, then the filter will be slightly brown or black even when cleaned.
Your owners manual should give you a good work description for cleaning the air cleaner filter with most telling you to tap the filter on a tire to remove the majority of crude in the folds of paper, then use compressed air with the tip 10" or so from the paper. As said, after cleaning check it with a flash light or shop light bulb to make sure it isnt damaged. Unless the external filter is damaged and allows dirt to pass to the inside filter, the internal filter may never need replacing. I have never seen one get dirt or black anything on the internal filter. Most of them can be washed also with soapy water- follow mfg, directions on this though as some may not be washable, but again every one I have ever seen is washable but dont wash it every time it is dusty, there is no need to wash unless they get oily or greasy like from a busted hydraulic hose that sprays oil into the air intake.
I think someone said they blow thru the inside using a leaf blower. I have never tried that so I wont comment on that, but compressed air will clean them and not damage. I have used the same filter on farm tractors for over 5000 hours and never had to replace it. As long as your internal filter is clean each time,you know you exterior one is doing its job. Black smoke from the exhaust when the motor is not lugging is a sign you went too long without cleaning, that and noticeable loss of power.
For those of you that want to replace filters, go ahead and buy new ones every time they look black or dirty. The filter companies love you, but these are not like throw away automotive filters that cost $5 each. The reason they are 30-60 bucks each( or even more) is because they are better quality and meant to be cleaned and reinstalled - even washed and reinstalled.
and WOW what a difference. The tractor has more power by a noticeable margin. The old filter was just filthy. What a dumb thing to forget about. 
