You may be familiar with air ducts that are constructed of sheet metal. However, many modern residential air duct systems are constructed of fiber glass duct board or sheet metal ducts that are lined on the inside with fiber glass duct liner. Since the early 1970's, a significant increase in the use of flexible duct, which generally is internally lined with plastic or some other type of material, has occurred.
The short answer is yes, duct cleaning, done right by a reputable company will help with the smell. It is likely though the smell is coming from another source, ie the crawl space. It could also be that another rodent is dead in the duct work. A visual inspection would be in order to check for any breach in the duct system. A duct pressure test would be able to tell you how much air is leaking from the system over all. A hole large enough for an animal to enter would loses a great deal of air, over 300 CFM. It would be worth looking into having this test done and it should cost around $200. Cleaning the air handler and evaporator coil will greatly improve the performance of the air conditioner. Dirt and dust on the evaporator acts as insulation and reduces the amount of cooling done be the coil. Any quality duct cleaning should include cleaning the air handler and coil, and the tech should allow you to watch him perform the work as it is done.
Be careful of dishonest HVAC contractors. There’s no magical formula to see if an HVAC contractor is scamming you, unfortunately, but remember that they typically do this in one of two ways: first, they are charging grossly low prices (far below everyone else), or second, they aren’t including what everyone else is. In the first situation, they will charge you change fees, other hidden fees, or they stole the equipment and are passing themselves off as legitimate contractors (very common in California these days). In the second situation, they are charging you a very fair price, but aren’t including what the other contractors are (i.e. charging $10,500 for the installation which is fair, but not including the ductwork which is a scam unless there is some other, complex stuff going on there).
I own an HVAC company. Dirt in your ducts stays there and hurts no one. It is like dirt on the ground outside. This industry was infiltrated by a bunch of money grubbing low lifes years ago. As a credible company, we do not clean air ducts. Some who were credible probably signed on not knowing what else to do or to try to make a buck another way. These companies, because they also do HVAC work not only rip off private homeowners, they are ripping off legitimate HVAC company's customers and the integrity of what can and should as a rule be a great service industry. Some probably have gotten into this to simply offer what competitors who were ripping off their customers were offering. Anyone cleaning ducts is in my opinion raising a big red flag that they cannot and should not be trusted. Political pressure from NADCA, advertising dollars, manufacturers and marketers of duct cleaning equipment, and intense competition for the customers is the only reason the government and adverstising companies have not run them out of business and that this cancer perpetuates itself.
I took off stars for two reasons. Minus one star for issues trying to use the $50 for $25 voucher I purchased through Yelp. Although there was no minimum stipulated, the office wouldn't take it for the initial $59 diagnostic fee. If I used the 10% off First service that they offer, then they won't let me use the voucher on the actual repair bill.  I was stuck with paying the full $59 diagnostic fee.
Contact/Relay -- Relays are electronically controlled switches that activate the various components of your HVAC system. They manage everything from the power going to the motor to automatic dampers, humidifiers, etc. Most of them are controlled by the thermostat. The most common failure for a relay is being stuck in the "open" position. Separated from its assigned contact point, it fails to complete the connection and send the message to whatever it was supposed to operate. This failure usually occurs from use over time. Each time a relay connects and sends its signal, the electrical arcing from point to point eventually causes wear and tear.

Ground source, or geothermal, heat pumps are similar to ordinary heat pumps, but instead of transferring heat to or from outside air, they rely on the stable, even temperature of the earth to provide heating and air conditioning. Many regions experience seasonal temperature extremes, which would require large-capacity heating and cooling equipment to heat or cool buildings. For example, a conventional heat pump system used to heat a building in Montana's −70 °F (−57 °C) low temperature or cool a building in the highest temperature ever recorded in the US—134 °F (57 °C) in Death Valley, California, in 1913 would require a large amount of energy due to the extreme difference between inside and outside air temperatures. A few feet below the earth's surface, however, the ground remains at a relatively constant temperature. Utilizing this large source of relatively moderate temperature earth, a heating or cooling system's capacity can often be significantly reduced. Although ground temperatures vary according to latitude, at 6 feet (1.8 m) underground, temperatures generally only range from 45 to 75 °F (7 to 24 °C).

Air duct cleaning service providers may tell you that they need to apply chemical biocide to the inside of your ducts as a means to kill bacteria (germs) and fungi (mold) and prevent future biological growth. They may also propose the application of a "sealant" to prevent dust and dirt particles from being released into the air or to seal air leaks. You should fully understand the pros and cons of permitting application of chemical biocides or sealants. While the targeted use of chemical biocides and sealants may be appropriate under specific circumstances, research has not demonstrated their effectiveness in duct cleaning or their potential adverse health effects. No chemical biocides are currently registered by EPA for use in internally-insulated air duct systems (see Should chemical biocides be applied to the inside of air ducts?).
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