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There would be only a few ventilation holes, so it could become very hot and sweaty after a short time. This is typically enhanced if the box is rubber lined such that the container is slimy and holds in any mess the slave make (during his toilet training), the air inside would be quite head with the smell of rubber (along with the stench of human waste if the dogs is a sewer pig as well).
Alternatively if outside it would be cold, of it could be the size to fit in the back of a Jeep should you wish to transport your animal to a new location (training camp), however be aware  of motion sickness and air vents getting blocked should the box move in transit -consider how you you get him out in a hurry, what if there was an road traffic accident, was the box secured ?
The box could also  be insulated from any other sound/vibration, maybe kept in a little used room or attic space; once use was to assemble a cage with in a attic eve space with no light, one door - it gets hot and humid in the summer and cold in the winter - either way there is no escape. This way the slave  would be totally isolated and know that there would not much chance of someone else hearing them. The slave would not necessary be tied up since he could not escape. The box could be used either for just keeping someone until required, or as a punishment, especially if it was very small and cramped.
It could also be included in a sensory depravation or mind control scene.  Here you have the option of isolating the box but controlling the sound supplying white noise or hypnotic suggestion loop tapes.  This was effectively used in one training program where the lined box had a few holes in it, the slave could look out of the holes, but the box was cantered in the room, the holes pointed to just the white walls. Using his best peripheral vision he could make out movement, he could hear (or think he hears) his guards moving outside the room. The Guards can see the box well both through the cell door (on the room) and also the box is monitored (CCTV+sound). It can often please a Master (and increases safety) to have the slave monitored at all times. This can be done using small spy camera in the box and a mic, so you can here his plight and begging, and promises of improved behaviour - but also for any other problems.
Note that this is a intense environment, so if drugs are used you have to consider the compound effect (paranoia, dehydration etc), though many boxes have dog-dish slots so you can slide in his food/water.

Cage Covers ^

If using his dog cage, a similar effect can be obtained (just like with bird cages) by putting a leather/rubber box cover over it. This would go close to the floor, but knowing that he might have a dog blanket in there, you might need to consider air vents. These air vents should be designed such that he cannot observe the outside world from there. A typical use would be when he is settling down for the night (and it is too early for you).  This construction should be for long term safe use. If there is poor air quality he will get headaches and his body will react - either way the scene ends, and you don't want a fatality. Since deep down a Master loves his dog, he will look after him and take reasonable precautions. The dog will get very used to the head space and remain where you put him - his context does not appear to change, where as yours is free to do so.

Also see http://www.geocities.com/WestHollywood/Heights/1163/prison.html