Heat and sunlight can do a significant amount of damage to your music stacks in no time making the records warp.
A warped record will sound 'woozy' and in worst cases will become unplayable. Generally, cold temperatures will not do any damage. However, sharp changes in temperature are likely to case moisture to condense on the record, damaging to the record, sleeve and covers.
Records should be stored:
1. Upright in a cool, dry place. No leaning allowed.
2. Far away from heat sources: the furnace, fireplace, dryer, etc. Otherwise, considerable warping and melting will ensue.
3. Away from sources of light, particularly sunlight (See No. 2.).
4. With the inside sleeve turned at a right angle to outside edge.
5. Preferably in a closed box or container to reduce the accumulation of dust. Dust is your enemy here.