Thanks for the additional information Andrew. No, I have never heard of or experienced this error with the R2400 or any other Epson printer model I've worked with...
I downloaded the Epson R2400 service manual (which I got here: http://www.gobookee.net/get_book.php?u=aHR0cDovL2dpZmluLnJ1L2ZpbGUvUjE4MDBfUjI0MDAucGRmCkRvd25sb2FkIFNlcnZpY2UgTWFudWFsIEFuZCBSZXNldHRlciBQcmludGVyIGF0IGh0dHAgLi4u), and do not find anything specific to "Fatal Error 42: Head Hot Error"- but do find two mentions of the paper feed and carriage mechanism causing "fatal errors".
It is possible that liquid, either from manual cleaning, or from the capping station drain tube(s) could cause issues if in contact with electrical parts- but if this was the case, I suspect you would experience this error at different times, and not just when the printer feeds a sheet of paper. The fact that your printer correctly preforms a cleaning cycle, and the print head can move back and forth the length of the carriage makes me suspect your problem is somehow related to the paper feed, possibly a gear out of place or something not moving correctly. The R2400 reference guide says the flashing ink and paper lights (at the same time), and power light being off indicates "Paper is loaded in the sheet feeder and the Front Printer cover is open."
If I were in your situation, this is what I would try:
1. Slide the paper width guide both directions to make sure it moves freely, open and close the front cover, and carefully examine all areas of the printer to look for misaligned parts, or something that would cause a jam error.
2. Push the ink change button to move the print head/cartridge carriage to the ink change position, then remove all 8 carts, close the cartridge carriage lid, push the ink change button to move it back to the right side (all ink out lights should be on), then turn the power off and unplug the USB cable. While the carts are out of the printer- check them to make sure the exit chamber is at least 1/2 filled with ink, no ink is leaking from anywhere (also check in the cartridge carriage to make sure there's no ink puddle that would indicate a cart may be leaking), and the air vent hole is open on all carts. After about 5 minutes, turn the printer back on, push the ink change button, reinstall the set of carts into their appropriate positions, close the cartridge carriage lid securely, then push the ink change button again. The printer should preform an auto cleaning cycle, ink lights should go off, and when it's done the power light should be on to indicate the printer is "ready". At this time, put a sheet of paper in the auto sheet feeder and push the paper feed button to load the sheet. Let me know if you get any errors at any point, or what happens.
I'm sorry for not being of more help with your strange error, but please do keep me posted and I will try my best to help resolve this issue and get you back to happily printing.
Best regards~ Dana