They seem more sensitive to temperature changes since they must expand and contract as a unit. With this style of instrument the sound board sits inside of the frame, which is usually exposed. The soundboard is held in place by the tension of the strings on the bridges and is free to expand and contract. I'm assuming you are a beginner looking to purchase your first instrument on which to learn. Rent one - great in theory but difficult to find in practice.
Some teachers have extra instruments they offer to rent to their students.
I don't know of any store that rents dulcimers. Purchase a used instrument - used instruments are hard to come by. If you can find one and can have someone who knows something about dulcimers check it out for you, this can be a good, less expensive way to get your feet wet. There is a web page devoted to used Hammered Dulcimers you can check out to see what prices are like and models are currently for sale. These instruments are smaller, lighter, and have fewer strings to tune.