Basically this is a means of transitioning companions,in this case from Mel to Ace. They both actually work together in this episode. It revolves around a character named Kane who is imprisoned on an ice world called Svartos. He is not above buying and even killing those who do his bidding. The doctor and Mel have arrived there only to meet up with the now broken Sabalom Glitz,sort of the Harry Mudd of Doctor Who if you know about Star Trek,who previous appeared in the sixth doctor stor y Trial Of A Time Lord. Glitz of course is looking to get his impacted ship back. The story revolves around Kane's attempts to get at the Dragonfire,a source of power held within a benevolent creature whose guarding Kane from escaping.
We met Ace here,real name of Dorothy apparently,as a dislocated waitress working for the Space Trading Colony. In the end Kane meets up with his comeuppance as even his allies begin to betray him,culminating in a final grotesque scene where his his face melts off before our eyes. In the end,for reasons mildly undisclosed Mel decides the now again dislocated Ace is more deal to be the doctors companion that herself,as she feels the need somehow to remain with Glitz to try to keep him in line. Overall it's a very clever and surreal story,with this oddly dressed little girl whom we never learn much about who seems to have some unknown play in the events that unfold.
Despite the fact the episode has a surreal and art David Lynch quality about it,it's rather sad to watch this episode on DVD and then see the depressing bonus features. Particularly saddening is one entitled "The Doctor's Strange Love",made by several rather mean spirited comedians who do nothing but ruthlessly make fun of the serial the viewer was just watching. Even the making of featurette "Fire And Ice',while providing many insights from the actors is filled with vitriolic mockery of the entire story,mainly it's association with the 1980's. In a way this actually helps us to understand the cultural schism's of the time that may have resulted in episodes like this being given such a harshly bad reputation. Taken out of the maelstrom of the era, this is an excellent Doctor Who episode and a good introduction to one of the more compelling companions in Ace.