Leopard gecko possibly sick

Question

Geiko   My daughter got a leopard gecko in December.  We live in Illinois and have been experiencing below 0 temps.  
The pet store suggested 10 gal aquarium with a heat mat in one corner.  We are feeding crickets only they did not suggest worms.  Geiko has been shedding but sometimes has trouble getting shed off.   We do lightly mist him with water daily.  

The other night Geiko was laying I the cooler corner of his home with his head turned and up against the glass.  His tongue was also out.  My husband picked him up and he was cold.  After Geiko was on the mat (we also turned on a space heater in the room) he came out of it.  Geiko is eating but not real well. He is also shedding.  Any ideas?

Answer
Your gecko is VERY VERY THIN. I would say it's emaciated.

Immediate suggestions:  Get a good thermostat.  The spot over the heat mat should be 90F, but very importantly, the temperature of the air inside the enclosure should be 80F during the day, and not drop below 70 at night.  You may need to add heat sources to achieve this.

Add a humid hide - a small butter tub filled with damp sphagnum moss, and a hole cut in the lid to allow the gecko to climb in and out, works well.  Keep the moss damp - change the moss often to prevent bacterial growth or mold. Be sure there is also a dry hide on the warm side of the enclosure.  The humid hide will prevent shedding issues.

Keep a shallow dish of fresh water available at all times.

Feed your gecko every other day, and feed it as much as it can eat in 15 minutes.  Remove any leftovers.  Be sure crickets and mealworms are gut-loaded with a quality formula, and are dusted with a calcium + D3 powder before you offer them.  Variety is best in the diet, and leopard geckos do well on mealworms, crickets, and phoenix worms.

Take your gecko to an experienced reptile veterinarian immediately.  It may be ill.  Illness caused by respiratory or mouth infections, or by internal parasites, is the most common cause of poor appetite.  Exposure to improper temperatures is a leading cause for contracting respiratory infections (basically, pneumonia).  These ailments are usually treated easily if caught early.  Based on its appearance, your gecko's condition is very serious, and it may need nutritional support to recover, whatever the cause is.

Leopard geckos store fat in their tails.  A healthy leopard gecko should have a tail that's about as wide as its body.  Here is an example:  http://acreptiles.com/avail/MaculariusNov2007/LG-N9.jpg
A thin tail means something is wrong.