Are there heavy armor with spellcaster stats? Or am I forced to use light armor to get the magicka stats?

You can make armour with magicka stats, however you will not benefit from the light armor passives.

Taking heavy armor is a trade off and a mage in light armour will be way more efficient as long as he is alive.

Perhaps I should've mentioned I was actually thinking of my templar destructive spellcaster. Since I see a templar mainly as a heavy armor class.

Same trade off applies. With light armour you could pull out more damage with less survivability.

Carry 2 or 3 sets of armour and experiment, go and kill some trash mobs in 1 set, switch out and kill same trash mob, rinse and repeat. This way you will find what works for you (and others when in a group) the best.

The only inherent difference between armor types is that heavy armor has a somewhat higher base armor rating than medium, and medium a bit higher than heavy. Otherwise, the stats available on each seem to be about the same. The effects of passive skills vary from one armor type to the other. Light armor passives generally provide magicka-related benefits while heavy armor provides defense benefits. It is quite possible to use heavy armor as a caster and bolster your survival that way as long as you have enchants that provide magicka/regeneration/etc boosts. It probably won't provide quite as much spellcasting benefit as the opposite approach of using light armor with its magicka-related passives and selecting health/resistance/etc-related enchantments, but depending on your build, it may still work.