We just bought a new tumble dryer. Disgraceful - they are environmental disasters, as we all know. And yet ....
Previous years, when we didn't have a working dryer, we had to crank up the heating in the house to about 21-22 degrees, so that the radiators stayed on to dry the washing. This year, the house hasn't had to be heated to over 19.5 degrees.
The dryer we bought is a condenser dryer. Nothing is vented outside. So any heat that is generated by the dryer remains in the house, which also decreases the load on the central heating (on a related issue, see my previous post about energy-saving lightbulbs here). The water from the washing is stored in a tank, which can be tipped away later on.
If there is an environmental issue, I think my concern is more the amount of fluff that comes off dried clothes. They must be wearing at a significantly greater rate, which means that they don't last as long.
Of course, there are certain parts of the world where dryers are hardly required. For example, I understand that Phoenix, Arizona has 350 days of sunshine a year. And yet every house has its industrial-strength dryer....