How can I keep the dryer heat in the house without the dust?
The dryer vents outside at present.
Given the cost of heating with fossil fuels and electricity, it is natural to want to recapture the waste heat from your dryer to reduce the demand on other home heating appliances. However, the short answer is -- you shouldn't.
First, if you are currently using a gas dryer, the air exhaust contains carbon monoxide and other byproducts of burning natural gas.
Second, dryer air contains moisture from the clothes being dried. This moisture can create very unhealthy indoor air quality and provide the moisture necessary for mold to reproduce on your walls and any surface in your home. For this reason the EPA Air Plus checklist includes verification for clothes dryers being vented to the outdoors.
While it may seem prudent and even environmentally conscious to recapture the heat from a clothes dryer, the side effect of doing so can be extremely harmful to your health. Your mention of the lint dust in your question is the first warning sign, but other consequences make this an even more dangerous proposition.