The red light is flashing and I can't resolve it. The printer is still functional, but I noticed that the paper is coming out very very hot.

What is the error that appear in the printer status on your computer?

check paper sensor it might locked by paper scarp

I hope this will help you :)
* Green Power light flashes- The printer is receiving a print job, replacing an ink cartridge, charging ink, or cleaning the print head.
* RED paper light is On- If the CD/DVD try guide is open, close the CD/DVD tray guide, load paper, then press the paper button. Your paper ran out or multiple sheets loaded at the same time . Load paper and press the paper butoon to resume printing.
* RED paper light flashes- Paper is jammed in the printer. Press the paper button to eject the jammed paper. If the light is still flashing , open the cover and remove all paper, including any jammed or torn pieces. Then reload paper and press the paper button to continue printing.
* RED Ink Light Flashes - One or more cartridges are low on ink. Check the message that appears on your screen to determine which cartridge is low, or follow the instructions in " Checking the Ink Supply". Make sure you have a replacement cartridge.
* RED Ink Light is ON- One or more cartridges are out of ink or not installed. If you have just installed a new cartridge, it may be incomaptible with the printer or incorrectly installed. Reinstall it or replace it with the correct cartridge
* RED Ink and RED paper lights flash alternately- The CD/DVD tray guide was left open when you turned on the printer or when printing on paper. Just simply close it/
* Green Power Light is Off; RED paperand RED Ink Lights flashing- Paper may be blocking movement of the print head. Turn off the printer, then open the cover and remove any jammed paper or other foreign objects. Turn the printer back on again. Or it may have an internal error. Turn off the printer, wait a few seconds, then turn it on again.

check the toner ,, check paper jam and ,, paper tray ,, or any sensor issue,, don't give the print order untill you see the green signal over the printer...

please use this URL http://files.support.epson.com/pdf/sc40ux/sc40uxpg.pdf to resolve this issue, and please revert either solve or not, Regards

There are actually some certain meaning on the red light and green light showing different information to user. The summaries are:
1) Green On, Red Off = Printer Ready.
2) Green Fast-Flashing, Red Fast-Flashing = Printer warm up.
3) Green Fast-Flashing, Red Off = Printer off-line.
4) Green Slow-Flashing, Red Off = Processing Data.
5) Green Off, Red On = Cover Opened, Toner Empty or Developer Unit / Drum unit missing.
6) Green Off, Red Fast-Flashing = Paper Jam or waiting for jam reset.
7) Green Off, Red Slow-Flashing = Paper Empty or Paper tray is not inserted.
8) Green Off, Red Off = Printer power is off.
9) Green Very-Slow-Flashing, Red Off = Printer in sleep mode.
10) Green (any condition above), Red Slow-Flashing = Toner low or paper empty.

So what is your printer condition? Better know what is going on your printer so can solve the problem.

Both red lights flashing? One should be for paper jam and the other for low/insufficient ink. I presume this is a deskjet/injet printer. The combination of these two lights flashing usually indicates a more serious issue rather than just low ink or paper jam. It is indicative of incompatibility of ink cartridge. After a while some cartridges just could become incompatible with the machine. All things being equal (i.e. no paper jam issue) a replacement of your ink cartridge will resolve this issue. Just get brand new ink cartridge/cartridges. It is usually ok to replace only the one that has become incompatible. But the issue is you need to troubleshoot to determine. You may not have the resources to do this, so better to replace both or replace one-by-one.

There are actually some certain meaning on the red light and green light showing different information to user. The summaries are:
1) Green On, Red Off = Printer Ready.
2) Green Fast-Flashing, Red Fast-Flashing = Printer warm up.
3) Green Fast-Flashing, Red Off = Printer off-line.
4) Green Slow-Flashing, Red Off = Processing Data.
5) Green Off, Red On = Cover Opened, Toner Empty or Developer Unit / Drum unit missing.
6) Green Off, Red Fast-Flashing = Paper Jam or waiting for jam reset.
7) Green Off, Red Slow-Flashing = Paper Empty or Paper tray is not inserted.
8) Green Off, Red Off = Printer power is off.
9) Green Very-Slow-Flashing, Red Off = Printer in sleep mode.
10) Green (any condition above), Red Slow-Flashing = Toner low or paper empty.

So what is your printer condition? Better know what is going on your printer so can solve the problem

YBC (/\)

There are actually some certain meaning on the red light and green light showing different information to user. The summaries are:
1) Green On, Red Off = Printer Ready.
2) Green Fast-Flashing, Red Fast-Flashing = Printer warm up.
3) Green Fast-Flashing, Red Off = Printer off-line.
4) Green Slow-Flashing, Red Off = Processing Data.
5) Green Off, Red On = Cover Opened, Toner Empty or Developer Unit / Drum unit missing.
6) Green Off, Red Fast-Flashing = Paper Jam or waiting for jam reset.
7) Green Off, Red Slow-Flashing = Paper Empty or Paper tray is not inserted.
8) Green Off, Red Off = Printer power is off.
9) Green Very-Slow-Flashing, Red Off = Printer in sleep mode.
10) Green (any condition above), Red Slow-Flashing = Toner low or paper empty.

So what is your printer condition? Better know what is going on your printer so can solve the problem.

YBC (/\)

Check the paper sensor has not come loose. Lift the lid, it is on the right hand side of the rollers with the red and blue wire. Press down lightly to make sure is hasn't come loose.

If not, reset the printer:
While the printer is on, press and hold the configuratuion button and press resume (paper feed) button 3 times.
Wait 20 second and press the power button.
Disconnect the power and wait 20 seconds.
Connect the power and switch the printer on.