I will be happy to help. What is the model number to your refrigerator?
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Did you remove the cover from the back of the fridge when you vacuumed the coils?
I don't feel you have a problem with your fridge. That warm area you feel between the two doors is meant to get warm. This is too keep the moisture off the cabinet and keep your freezer gasket from freezing to the case. Things that could cause this to get Hot:
Condesor fan not running when compressor is running
Defrost issue where compressor is running constantly.(check for frost of rear freezer wall)
Low Freon, compressor will run constantly to keep temperature
Freon restriction, compressor has to work to hard to not cool enough.
Let me know if this helps you out. If you have anymore questions, please feel free to ask. I am a Factory Authorized Servicer for Electrolux/Frigidaire, I work on your type of machine on a daily basis.
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Your refrigerator is probably fine. If its not hot to the touch. The temps are ok. I would only suggest having someone take a look if you feel the fridge is running more than 60 percent of the time, in average 70 degree room temp at factory settings.