I have a Brother HL 5340D printer. I have around 6-7000 pages to print.
I want to know how many pages I can print continuously. Will it heat up?
You should be fine!
In general the main thing that heats up in a laser printer is called the fuser. The fuser usually accounts for the majority of a laser printer's power usage. The heat of the fuser, under substandard conditions, can definitely cause damage to interior parts, however newer printers will usually have a good ventilation system to aid in heat dissipation. Another feature of newer printers is a power saving feature which will turn off the fuser and let it cool down. The printer only starts up again after proper working temperature is reached. You'll know if you have this feature or not If you've ever printed 100 pages or so. The stops are very noticeable but at least you know it's for safety reasons.
The HL 5340D specifically is from early 2009 I believe. It more than likely has these features and then some. You can even see the abundance of ventilation area they've given it on the sides:
It has these specs:
Max. Monthly Duty Cycle: 30,000 pages & Recommended Monthly Print Volume: 500 to 3,500 pages
So, I think you should be fine. It will get heated up, but that is normal for a laser printer. That is what fuses the toner to the paper. It should heat up to its normal operating temperature and stay there. It is kind of like miles on a car, it is wear and tear, but it doesn't matter that much if you put them all on it in a year or 10 years.
This shouldn't be an issue for a printer of this caliber, though it may result in more wear and tear than you'd want.
The monthly duty cycle limit is 30,000 pages, with a recommended monthly duty cycle of 500 to 3500 pages. The sort of print job you're running can be very stressful on the printer; I'd suggest that you allow the printer to cool down for 10-15 minutes every 500 or so pages.
Note that the high-yield TN-650 toner cartridge has a specified yield of 8000 pages and the DR-620 drum unit has a specified yield of 25,000 pages.