The Rage Mage

A Half-Orc yells as a barrage of Scorching Rays fires from his eyes, obliterating a wolf. 

An Aarakocra lets loose a swarm of Magic Missiles to decimate a gang of Bandits that stole their lunch.

A Goliath lets loose a ferocious Burning Hands to incinerate a swarm of bees.

A Rage Mage is a Wizard who uses the anger within them to channel magic into the world. The verbal components in their spells could take the form of yells and screams while they throw themselves into the heat of the fight. They typically clad themselves in furs in place of typical Wizard robes to signify their primal style of magic and use blood to inscribe spells into their tomes. Rage Mages use a system of forced magical pulses that summon a random effect to protect them and harm others. This magic is sourced from the primal anger stored within every intelligent and unintelligent creature.

Intellectual barrier

As an action, you can give yourself temporary hit points equal to your wizard level + your INT modifier (minimum of one temporary hit point). You can use this a number of times equal to your proficiency bonus per long rest. This lasts for 10 minutes

In the Thick of Things

Starting at 2nd level, spells that you cast with a range of touch or self (excluding the spells that impact you) have advantage or disadvantage on the target if appropriate. For example, a casting of Burning Hands would lead the opponent to have Disadvantage on the saving throw. A casting of Fireball would not do this.

Magical Pulse

Starting at 6th level, you can dig deep and cast a ferocious version of a spell.

Pick four of these options to add to a table. Roll a d4 when you are choosing which one will activate.

• Magic missile casted at 3rd level. 2 of these magic darts must hit an ally (you choose who, it can be yourself) and 3 hit an enemy target.
• Burning hands is casted at 1st level in a direction you choose, you must make the saving throw as well, but on a success you take no damage. This is impacted by In the Thick of Things. in the way that is favorable to you.
• You and a target that you choose is now under the effects of Enlarge/Reduce. One of you is enlarged, one is reduced. This is decided by a coinflip or a roll of 1d2 attempting to predict the outcome, you choose who is enlarged in a successful guess.
• You cast Poison Spray in every direction.
• You cast Scorching Ray at 2nd forward, 45° to the left and to the right of that forward beam. This is casted from your eyes and mouth. This can hit allies. 
• You cast Web at 2nd level but you must be inside the casting area.
• You cast Witch Bolt at 1st level. roll a d4. On even numbers, it hits an enemy target and on odd numbers it hits an ally of the DM's choice
• You cast Chromatic orb at 1st level. When it is summoned, it remains in place as a trap, when anyone touches it (friend or foe) it automatically hits.

When you use your action to use a Magical Pulse, you roll a d4 and pic the corresponding magical effect from your table of four. You can do this a number of times equal to half your proficiency bonus (rounded down) per long rest.

Magic Muscles

Beginning at 10th level, you can use spell slots to boost your physical abilities.

For every spell level that you burn you can jump 5 feet up or in a direction, push someone 5 feet per spell slot in one direction (they can make a CON saving throw to move half the distance) or throw something 5 feet per spell slot.

This is an action.

Adrenaline

At 14th level, When you reduce an enemy's HP to zero with a spell affected by In the Thick of Things, you can choose to restart your turn. This includes movement and anything else that you could have done on your turn. You may do this a number of times equal to half your proficiency bonus per long rest and this ability can be used more than once per round. You regain a use when you kill an enemy of significant threat (DM's discretion)