I know nothing about strawberry seeds so can't tell but probably works similar in their brain :)

If you don't get frosts and snow there, you could probably keep it outside all year round. Just make sure it doesn't get too much rain, and NO RAIN in winter when its colder (like below 10).
In summer it will love the warm weather and sun.
Most cacti can stand up to zero degrees and even below zero for short time if they are kept completely dry. The moisture is deadly when cold as they will simply rot.

If not - leave it some colder place for a month or two and do not water. Most will stop growing in the fall when they feel its getting colder. That's when I stop watering mine and will not water until around February when temp is starting to reach about 12-15 degrees. But I keep mine outside all year round.
Garage probably could work if cold enough and only after it stops growing. If it is warmer it will want to grow and with low light it will stretch and deform.

Do you know what cactus it is?