Why is my character exploding in funny way at render time.

Have you check your character's joint hierarchy? This issue usually happens when the root of your character is under a group already scaled. All the nodes above the root bone (transforms, controllers) should have a identity scale (1., 1., 1.) 

Also please check if Scale Compensate option is not activated on some bones as described here. Once Scale compensate is disabled on every joints and the parent group is scaled back to 1,1,1 don't forget to export back your fbx!

 Please refer to this documentation page for more information about character prerequisites.