I'm not clear on where the bookshelves will be, you have doors on the right. Plus you have bookshelves next to the fireplace, what happens with those? Is your primary intent to cover the white box, or mainly to have more bookshelves?

What type of heater is that? Radiator with hot water, or electric? Both will need some vents a) to work and heat the room and b) not to overheat the cover you want to put on it.
It seems you are looking to make two thin tall cabinets either side of the radiator. So how will you deal with all the plugs and the sensor above the radiator. Do you plan to move these or integrate them into the cabinets?
Let us know so we can help.

I need something to cover the heater firstly...The heater is radiator with hot water and my neighbor who has exactly the same house,made a library and covered the heater (just there we do something like panel with holes ,so the heating can circulate).the library next to the fireplace will be used for our home cinema & our hi-fi stereo and books...but i desperately want to do something in this space .I hate it like that...my neighbor's is lovely but is a wooden library custom made exactly fitted for this space.But i don't want to make too "heavy"...

and i intend to leave the plugs as they are and NOT cover them...whatever i do i will do it next to the plugs..or i can fit them into the cabinets...but how should i do it????

Fine - it sounds as if the panel idea with radiator vents will work fine. So basically you can build a "single unit" of three different depths to create one cabinet. I would add three doors to the lower part (two for storage either side) and one in the front as the vent for the cabinet. You can then create shelves.
If you have a good electrician (here we would need fireboxes for the plugs against wood) you can feed the plugs into the sides of the wood cabinet so you can make it wider
Below is an example of the cabinet (doors along the bottom; middle will have a vent - will find examples) and then shelves along the top.

We frequently bring outlets and switch boxes through the backs of cabinets...have to in kitchen sink bases as all disposers and dishwashers must now be installed with plugs. Moving an outlet to the front of the cabinet will require more work, as the original box will become a junction and must be left exposed (it can have either an outlet or a blank cover plate). My advice is, if you like your neighbors solutions...take some pictures and get a cabinet maker to give you a quote!

I was just thinking the same thing Ironwood !! the neighbour could possibly introduce you to who made theirs !

I agree with Ironwood and OnePlan. Talk to your neighbor. Get as much information as you can. Tell them that you really like their bookcases and want to do something similar in your home (not copy theirs exactly). Ask if you may take photographs of their bookcases. Ask them who built them, what they are made of, if there are any special details that the casual observer would not notice. If possible, take measurements. You might be able to get your neighbors enthused about your project, and they might help you build yours!

Thank you all so much..I will do that..I will go and take a picture of his library..thank again:)))

here are some ideas

This is how he did but he moved the heater to another place,where I have my other library.so for my place should be something like that with different middle bottom(in order for the heating to circulate) and if course another style to suit more properly my home style and the other library..

That's great - so something like this for the radiator could look very good
http://www.westchesterwoodcrafters.com/radiator%20covers.html

That is great!!!thank you for the ideas.I will use them for my custom made library..

I would build a tall floor cabinet book shelf depth and put two floor to ceiling doors on it. I would then frame the doors and then find a modern metal mesh insert to place on the doors. Also place lights inside the top of the cabinet and use glass shelves. Top would store books and bottom would allow heat to circulate and it would be concealed and very finished. then it would not detract from the fireplace wall. I think you can put in puck lights that come on when you open the doors and go off when you close the doors. You can find all styles of vented metal sheeting these days in many finishes from brass to black to gold to silver.

Why not copy what your neighbor successfully did ?????????????? !!!!!!!!!!!!!!!!!!!