To ensure that all is well, you should respond to your nose's early warning, using it as a sign that something is amiss and checking all possible causes.
Check Heating Vents
Particularly if this odor is originating from a stuffed-to-the-gills closet, one possible problem could be that something is blocking your heat register. Sift through your closet and locate the source of heat in the space. Ensure that this vent is completely uncovered, moving items as necessary. For example, if some clothing is hanging nearby that sometimes obstructs this vent, find a new home for these garments.
Inspect Closet Lighting
Another potential issue related to your closet is lighting. Check over the lighting in your closet, ensuring that you don’t have anything pressed up against it. If, for example, you placed some plastic boxes on a top shelf and they are a bit too close to your light source, these boxes could be getting scorched, leading to the burning plastic smell. Because this is a potential fire hazard, dealing with this lighting issue immediately is a must.
Look Over New Electronics
In some cases, burning plastic smells can come from new pieces of electronic equipment. If you have a brand new TV or DVD player sitting close the closet, this could be the source of your odor. If the source is a new piece of electronics, you don’t need to do anything to remedy the issue, but instead simply continue to use the new tool. If, after several days, the smell has not dissipated, contact the manufacturer and report the problem.
Have Wiring Checked
If all your checking finds no obvious culprit, you should have a professional check your wiring. It is possible that a piece of wire somewhere deep within your walls has become frayed or a connection has been compromised leading to this smell. Because a wiring problem can easily result in a fire, having this issue checked immediately is in your best interest.