One of my students spelled the word <refrigerator> and I thought he was wrong. We checked it with a dictionary and found that my spelling <refridgerator> was incorrect. I thought it was correct based on the knowledge of using <dge> after a single short vowel phoneme. Based on my previous quests, I told him that I don't think this spelling could be explained by phonics. So we began, our investigation.

Here was our word sum:

refrigerator -> re+frig+er+ate+or

I looked up the word on etymonline:

refrigerate (v.) Look up refrigerate at
1530s, back-formation from refrigeration, or else from Latin refrigeratus, past participle of refrigerare "make cool or cold." Related: Refrigeratedrefrigerating. Earlier words in the same sense of "to make cold, to cool" were infrigideninfrigidate(both early 15c.).
We noticed the latin <refrigerare> and looked it up in our latin dictionary and got the root <frigere. So I'm assuming, based on my limited latin skills, that the base we're using is <frig> from the root frigere "cold". This explains the <g>. 
So he asked me this question:
Why wouldn't English spellers change the way we spell this base to <fridge> like in the spelling we normally use? Why wouldn't we change the <g> in <frig> to <dge> so it's consistent with the <dge> spelling convention?
"I put the food in the fridge." 
He said this spelling <fridge> makes more sense. Can anybody help us make sense of this word?