I'd heat it up real good and hit the grill with a wire brush.  How dirty we talking here?  Black mold or just burnt food?

Where is our resident expert Shamb?   

I find that with gas grills people do not preheat enough.  A thermometer on the lid/hood is useless as far as I'm concerned.  The temp on those gauges show air temp not the metal grill temp.  I like to see that thermometer at least 600 degrees or go "full circle".

I would super heat it and then brush it.  It you get it hot enough the old food crude should turn ash white. 

I always give a quick brush after each grilling session.  When I use it again, I super heat for the proper grilling temp,  but also to clean.   It makes more sense to me to do a fast clean after cooking.  Then the next day, you preheat and clean.  That way you really burn off the gunk and get the metal good and hot. This kills two birds, and hopefully makes you feel better about running it wide open for 40 minutes before dropping that steak. 
 
Torch that thing!

And we are talking grilling not true BBQ.  I'd still heat to clean, but most gas grills can't go low enough for true BBQ.

Shamb?  Bueller?

I'm into some Evan Williams....Is that as clear as mud?
 

Yea use a putty knife and scrap off all the thick stuff then get it as hot as you can, let most of it burn off and hit it with a wire brush. You don't want to clean it until it's "shiny and new" you worked hard to build up that residue which is what you want to ensure it doesn't rust.


It's called "seasoning"

Sometimes one or two of my BBQ's will sit for a year or so.. and it smells horrible but once you heat it up and scrap the inside it's good to go.. no need to get it really clean.

mine is past seasoned.... tis just nasty at this point..... i'm not in a huge hurry to clean it though, have a lot of other stuff I am working on before that