I doubt that anything will have to be destroyed but if unclean things were to enter into the Temple it would be desecrated and need to be closed till it can be rededicated.  
 
Absolutely no one that is not member of the Church with a current Temple Recommend can enter the Temple. In fact Temple's have emergency plans in place in case of medical emergency to have trained temple worker's assist in moving a sick or injured member out of the temple to EMT's who are outside the temple.  
 
I have even heard rumors that in Utah where the membership is in the majority that many fire districts with a temple have a team of fire fighters/emts that are always on call that are endowed temple recommend members in case there is a medical or fire emergency so that they can enter the temple.

Heavenly Father loves everyone, he loves them so much that he protects them from the consequences of entering sacred places unprepared.  
 
We always invite everyone to worship the Lord with us in our meetinghouses and get closer to Heavenly Father and Jesus Christ. The Temple though is not the place for finding Heavenly Father though, it is the place where we receive sacred ordinances that teach us about the plan of salvation that only those who have spiritually prepared for are ready to receive.  
 
To enter the Temple unprepared is a serious transgression and a mockery to Heavenly Father, and Lord will not be mocked. Only persons who have devoted there entire life to living the commandments and have spiritually prepared are ready to enter the temple and do the ordinance work for themselves and there deceased relatives.  
 
You are right you may never step inside the sacred areas of a Holy Temple in this life, I hope that you do have the change through membership in the Church and spiritual preparation to enter the temple to be able to do so, but not everyone will have that chance in this life. Not even every member of the Church will have the opportunity to do so due to spiritual or other concerns.  
 
Not being ready to enter the temple is not a sign of shame or lessen the Father's love for you, all will have the opportunity to receive the blessings of the Temple in this Life or in the Spirit World should they prepare and choose to accept the promise required to obtain them and obey those commandments for eternity.

I'm the only member of the Church in my family and I'm getting sealed to my fiance in an LDS temple in June. 
 
My family doesn't understand why they aren't allowed to go see me get married and I don't know how to properly explain it to them. I've tried a couple times but telling them that temples are holy places, houses of the Lord, and only those who are worthy can enter doesn't seem sufficient enough. 
 
Can anyone help me with a better explanation to tell my family that will help them understand and not offend them?

Marissa - I would suggest that you have a small ring and committment ceremony after the Temple Wedding that your family can attend. You do not have to exchange rings in the Temple but could do it later that day when your family is present.