Freezer not cycling on
Fridge freezers (the common type with a single compressor) are often designed in the assumption that a certain amount of heat will leak into the fridge, i.e. they have a minimum operating temperature of a cool room temperature.  They can't control the temperatures of the fridge and freezer completely independently.  Some models only have one thermostat, while in others cold air from the freezer is circulated through the fridge and back to the freezer, putting a load on the cooling circuit and turning on the thermostat.

You can sometimes work round this by pressing the "fast freeze" button if you have one.  This will force the freezer to run, but may slow down defrosting.  

Wrapping the defrosting items in a thin insulating layer will also mean they defrost more slowly, and cool the fridge less.  

Starting the defrost at room temperature would avoid this but you have to be careful to not end up with outer layers sitting around at room temperature.

A good compromise may be to start defrosting at room temperature, then transfer to the fridge when the outside of the frozen item is still around freezing point.  A light insulating wrap will slow this process down and make for more uniform defrosting; you can leave this on when you transfer to the fridge.  You would probably be talking about quite a few hours at room temperature, especially if it's multiple packs you can rearrange when you check to make sure they're still frozen.