It does have the exposed heat sink and IIRC no fan. It's not that big, smaller than a FT-1802 or FT-79/88/8900. About the same size as the current FT-1900 I think. There's not much empty space in the case, it's a very small radio.
Good little radio, worth hanging on to for when you get your ticket. Probably worth $75 to $100 on eBay or eham.com, I'd likely ask about $50 from a friend if it's in nice shape and functions.
I've always thought the guts of the Kenwood TM-241 are probably the same as the FT-2200, although I've never had both at the same time to compare. They seem /very/ similar.