Not all ice is created equal. The thinner/more fragile the ice the more likely it will be susceptible to quick bursts of heat. A delicate ice sculpture might suffer some deformity but a wall of ice 5' thick might barely do anything other than get a bit more slippery from such a blast.
I hope that I would decide to make it, initially, a partial success for the player leading to a complete success over some reasonable time span that is interesting story - wise.Like, the player is casting fireball in an area covered in a thin sheet of ice and wants it to melt the ice. But the DM thinks the explosion is too rapid to impart enough heat to actually melt the ice. What then?
That is actually a good point, from a "physics" perspective. Having melted ice with a "Tiger torch" (big propane torch), melting any significant quantity takes a LONG time. Not only does water take a huge amount of energy to heat, but the heat of fusion soaks up a lot as well. There is also the fact that it is hard to melt ice with radiant heat, have had plenty of bonfires on ice or in the snow, and it is surprising how small of an area is effected.
If the fireball is being compared to "real" fire and the duration is "instantaneous" then it is hard to imagine anything more than a very thin layer of ice melting. That is all that happens with a propane gas explosion for example. It would have to be some magical property of the fireball that would allow it to melt any real quantity of ice.
Of course, that is the physics of the situation. What it really comes down to is the GM's ruling and whether or not it works or is "cool" for that time/place/game.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.