How can I make good use of the Fire element?

Fire as a Barrier

Shield + Rock + Rock + Rock + Fire : Makes 3-strength rock wall, with fire. People close get set on fire, and the rocks are harder to break though than 1-strength rock, and you need to extinguish them first.

Fire as a propellant

Arcane + Lightning + Fire : a good spell before having to use steam, minimal key combination effort for pesky goblins, especially those with a sack'o'bombs. Also good for when you cross beams with an Arcane + Lightning + Cold. Ka-boom!

Fire as a projectile

Sometimes you have an icy river separating you from the bad guys. Know what's good? Rock + Fire + Arcane. A boulder of firey goodness. Throw, explosion, ice melted, bad guys drown.

And the best use...

Fire as a soother of souls

There is no better way to cure the common cold (or a wet wizard playing with ice) than a bit of self-casting flame. Warms you up good and proper.

I'll add an answer since no-one has mentioned this:

If you get the grease spell early in the game (over the water to the left when you leave the starting area), you can cast grease and then set it on fire using a basic fire cone. This actually deals a reasonable amount of damage to anything standing in it, and isn't cancelled with contact with another shield spell.

The best use for Fire as an element in spells is to set explosives on fire. When faced with large numbers of goblins, some of whom are carrying bombs, a mix of Lightning and Fire will allow you to set off a chain reaction that will kill most of them in short order, without actually needing to aim the spell.