You will not be able to generate enough heat to kill bed bugs in your apartment using the method you describe. The problem is that you actually need to go to about 130F to 140F to penetrate the walls and mattress etc.
Unfortunately there isn't a simple solution to your problem. I'd suggest the following:
1. Contact the local department of health and human services in your area to see if their are laws that will help you. Some government agencies will work with landlords to prevent a bed bug problem from spreading. It's not just your building, what if visitors spread bed bugs to other buildings.
2. Protect your bed as best you can. This includes treating the bed with a spray (see resource for suggestions), and then encasing both the mattress and box spring with a bed bug safe cover. Pull bed away from all walls and furniture by at least 6 inches. Make sure all blankets etc. have been washed and placed in dryer for about 30 minutes on high heat setting. For added protection use a hand steamer along seams or if you don't have one, use a hair dryer for 30 seconds per location, at low air, high heat setting. Be sure to treat the bed frame as well. Use the resource below to create your own trap under each bed leg (or buy a version of the Climbup traps in resource). If you have double sided tape, wrap around each bed let for added protection.
3. Use your vacuum. With a small wire brush, remove bed bugs in all mattress seams and cracks around the room. Use the crevice tool if you have one. When done, remove vacuum bag in room being treated and dispose outside the home.
4. Declutter your home. Throw out any magazines and newspapers the room being treated. Store what you can in plastic containers with a snap lid, or buy inexpensive Ziploc big bags to store clothes etc. These bags are bed bug proof and can be had for under $10. If you can't find them in the store, there is a resource in the source below.
More tips can be found in the source. Until you come up with a whole building solution that addresses the problem in the apartments next to y ours, including those above and below, this problem will not go away. However the tips described will help to some degree.