This is just me, but I personally only use a paper towel to wipe the inside. When it gets caked with smoke I use a plastic putty knife to knock of the loose crud. I've heard of others using old or sample credit cards for this.
I do like to take some vinegar and clean the internal probe every other month and at this time I take a 12 gauge shotgun wire cleaner and run it up and down the top hole to clean it.
Another tip is, I've learned to use the disposable plastic food glues while doing this.
After 15 months of hard usage I can honestly say that I've cleaned the outside twice with cleaner, but NONE has every been close to where my food goes, but to each his own!