How can I fix a bleached stain within a mat? I had a reptile tank beside an under tank space heater on...

I had a reptile tank beside an under tank space heater on my carpet and it seems similar to the constant heat from the pad lift the color from the rug. I see by reading other answers that there are ways to dye it back. Does anyone own any idea how much it costs to dye it? The spot is no larger than 1 sqft, and the carpet is a insightful ply typical apartment beige.
Thanks!
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Answers:    I don't know how to dye carpet to be exact installed but I would think you would have trouble equivalent the color so I would recommend a repair. Look to see if there are any scraps of mat left over from when the carpet be installed and cut a square around the burn mark and then a cut a square of the square to fit in to it. Use carpet cassette to but the scrap in as a patch. Make sure to read the instructions on the cartridge and do not get the type that requires a steamer. Try this link for step by step photos: http://www.diynetwork.com/diy/fc_carpets... Also if in attendance are no scraps you may be able to budge to a carpet store or Home Depot with a indication and get a remnant.

If you are a renter chances are your innkeeper used a very common runner when he or she installed and this might make finding a match effortless.
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If you can cut a small sample of the carpet from somewhere it will not be notice, you can take it to a fabric store and hold them match it with a yard goods dye. I did this once in an apartment I was renting beside a dark beige hearth rug. The match was in the region of 95% I would say. Close enough to not be visible from more than couple steps away.

Aside from that you would have to replace the patch of carpet, which depending on the age and wear of the mat may be difficult to match up with a patch.