i think you are over thinking this.
We routinely dry our washing on the "pulley" Contrary to popular belief this does not add a noticeable amount of moisture into the house, there is no condensation or mould anywhere. And I cant say it has any effect on the temperature of the small utility room that it is in. So just do it and don't worry.
If you use a non condensing vented tumble dryer, you, like me, will cry at 3KW of heat going out of the house through a big hole in the wall. If you use a condensing dryer, it will use much the same amount of energy but most of that stays in the room so adds to the heating of the house. You might detect I am not a fan of tumble dryers. the sole purpose of ours is to make the towels and socks "fluffy" and experimentation has found for that you don't need to dry them in the TD, just partly dry them, then hang them on the pulley to finish off.