ASA Objekt gets too cold and stretches  

RE:

Unfortunately, that's physics. Everything shrinks as it cools (except for a few exceptions like water cooling from about 4°C to 0°C). Some materials shrink more when cooling. ASA shrinks enough when cooling that can create stresses large enough to curl the print and sometimes separate layers when there is a temperature gradient top to bottom.

You can try using a draft shield to try to keep some of the radiant heat from the bed at the sides of your print. It might help or it might not be enough. Alternatively, you can find a large enough cardboard box to cover your printer (and presumably the filament on top). You can use this as a temporary enclosure by lowering the box over the printer once you are ready to start printing.

If you aren't sure how to turn on draft shields:

1. You need to make sure the mode pull-down in the upper right-hand corner is set to either "Normal mode" or "Expert mode". Both of the settings you need to change have the yellow normal mode dot next to them.
2. In Print Settings, select "Skirt and brim" on the left-hand list.
3. In the "Skirt" pane, set the "Loops (minimum)" are set to at least 1. (I used a draft shield once to play with the feature a long time ago and found that 1 loop draft shields don't hold their shape well for large objects, so I would suggest setting the loops to at least 2.
4. Also in the "Skirt" pane, set the "Draft shield" pull-down to "Enabled".
5. Now when you slice you should see a wall all the way around your object. Unfortunately it isn't form fitting if you have any concave walls on the side of your print.