Since mite allergens are so stable, they can last in a carpet or bed and cause symptoms for years. Air conditioning has been shown to be an effective way to reduce mite populations in a space. The most likely mechanism is through reduction of relative humidity . Dehumidification of basements in summer and heating in winter, since both reduce relative humidity, are useful ways to limit dust mite populations. One mistake made by many homeowners with finished basements is keeping temperatures excessively low during times of non-use.
Low temperatures result in high relative humidities that foster mite population.
Though I find nearly all basement carpets irritating, those that are the least bothersome are in basements that are kept unintentionally warm by boilers operating in the summer to heat the domestic hot water. Dust mite allergens are carried on fecal pellets about 25 microns in diameter. These particles are normally not airborne. Any attempt to reduce mite allergen in the air with an air purifier is in vain. The allergen is only airborne briefly after disturbances.