No shelf above the TV and no boxes on either side - where exactly were you expecting the cat to wind up?
Cats like to be high up - they like to be warm - they like to sit in boxes (they feel safer that way). So put a warming pad in a box on a shelf, above the TV - and your cat won't be in your way anymore.
You can skip the warming pad if it is warm enough - and if boxes look too tacky you can get a cat bed like this - cats like them even better than boxes. Put it on a shelf over the TV and you are all set.
Probably cheaper too. I did find this one, not technically heated but it reflects the cats own body heat to warm the bed up.
My cats LOVE this one!
Aspen Pet Self Warming Beds https://www.amazon.com/dp/B00DJRCQBW/ref=cm_sw_r_cp_api_glt_fabc_qcI2FbE985M17
Luckily I just typed this out for someone in another thread! I have a strategy that has worked 3 times before. I had 2 cats already, acclimated a 3rd permanent and have since acclimated 2 fosters (one was here for 9 months, the other 5):
1) Choose a bedroom that will be the 3 year old's (preferably the one you sleep in). This bedroom will be closed at all times, the 3 year old will be restricted to this bedroom at all times and the other cat is not allowed in. This is now the 3 year old's territory. As she spreads her scent around she will grow more confident (which is a necessity if you want her to get along with another cat). This room should obviously have its own litter box and food/water bowls.
2) Put the 2 cats on the same feeding schedule. Do not change either diet at this time, continue feeding them the same food(s) they're used to. Feed both cats on either side of the door as much as you can. Food is a positive interaction, this is to start building positive associations with each other now that they each have a space of their own.
3) After at least one week has passed (please don't bother trying to rush the cats, just let time do its thing) put up a pet gate. I have this one that's $10 at Walmart. Yes, the cats can jump over it but they typically won't because they both know the other side is another cat's space. And if they do jump over you should be immediately putting them back on their own side. The gate should be up 24/7, when you are home. If you leave for any reason take the gate down and close the door. Continue feeding them next to the doorway, the gate now allows them to see each other when they eat instead of just smelling. If you have treats you can also hand them out by the gate for another positive interaction.
4) After another week has gone by you can test the waters by taking down the gate. Only under constant supervision, of course. One of the cats will probably start exploring the other space while the other watches. If there is any negative behavior be sure not to punish the cats. They will associate any negative behavior from you with the other cat. Positive talking and petting only. If things go well, great! You should still separate them into the appropriate rooms when you're not there until another week goes by without issue. Continue feeding them in the same place, remember no changes during this process. You want the 3 year old to still have her complete "safety room" whenever she wants. At night separate the cats as well into the appropriate rooms (3 year old = bedroom, other cat = rest of the apartment). If there were any negative behaviors beyond a little hissing, put the gate back up and just continue #3. Some cats take longer, some shorter. Doing this 3 times I know exactly how long it takes for my cats to warm-up to other cats, 2 of them just a week but the 3rd is very defensive and needs the full 3 weeks before she's on "speaking terms" with a new cat.
Cats are very particular about their space and other cats entrenching on it. Cats going into new environments also need to build up their confidence by having a space of their own. Both cats will be very defensive at first because of this which is why such slow introductions are necessary.
My 3rd permanent cat was adopted from a shelter at 2 years old, she spent her entire life there from when she was just 6 weeks. She is still fearful and skittish but getting better every day. Under the bed was her safety zone for the entire first 2 weeks. I just gave her the time she needed and all the affection I could. She eventually outgrew the "safety room" and now her favorite place is in the living room. The best tips I can probably give you for a skittish cat is to make sure they have access to everything in a comfortable space for them. Right now, it's the bedroom for your 3 year old. After this process is over she may pick a different place like what my cat did. It's a great idea to make sure she has a litter box and food/water nearby. My cat also has her own bed in the corner, she's the only one that likes beds so I think it has to do with feeling protected (it has sides like this one, I'm upgrading it so it has a roof too like this one.
I hope this helps, if you have any questions feel free to ask!