Scene change and day night cycle

The simplest approach is to use DontDestroyOnLoad on the object that is responsible of the night/day cycle. That function allows you to "save" that object between scene changes, and, as a consequence, also the variables referred to its scripts. I know that is nothing more than a starting point, but without see your code is all that I can say!

Here is my code:

 using UnityEngine;
 using System.Collections;
 
 public class GameTime : MonoBehaviour {
     public enum TimeOfDay{
         Idle,
         SunRise,
         SunSet
     }
     
     public Transform[] sun;
     public float dayCycleInMinutes = 1;
     
     public float sunRise;
     public float sunSet;
     public float skyboxBlendModifier;
     
     private const float SECOND = 1;
     private const float MINUTE = 60 * SECOND;
     private const float HOUR = 60 * MINUTE;
     private const float DAY = 24 * HOUR;
     
     private const float DEGREES_PER_SECOND = 360 / DAY;
     
     private float _degreeRotation;
     
     private float _timeOfDay;
     private float _dayCycleInSeconds;
     
     private TimeOfDay _tod;
     
     // Use this for initialization
     void Start () {
         _tod = TimeOfDay.Idle;
         
         RenderSettings.skybox.SetFloat("_Blend",0);
         
         _dayCycleInSeconds = dayCycleInMinutes * MINUTE;
         _timeOfDay = 0;
         _degreeRotation = DEGREES_PER_SECOND * DAY / (_dayCycleInSeconds);
         
         sunRise *= _dayCycleInSeconds; 
         sunSet *= _dayCycleInSeconds;
     }
     
     // Update is called once per frame
     void Update () {
         sun[0].Rotate(new Vector3(_degreeRotation, 0, 0) * Time.deltaTime);
         
         _timeOfDay += Time.deltaTime;
         
         if(_timeOfDay > _dayCycleInSeconds)
             _timeOfDay -= _dayCycleInSeconds;
         
         if(_timeOfDay > sunRise && _timeOfDay < sunSet && RenderSettings.skybox.GetFloat("_Blend") < 1) {
             _tod = GameTime.TimeOfDay.SunRise;        
             BlendSkybox ();
         }
         else if(_timeOfDay > sunSet && RenderSettings.skybox.GetFloat("_Blend") > 0){
             _tod = GameTime.TimeOfDay.SunSet;
             BlendSkybox ();
         }
         else {
             _tod = GameTime.TimeOfDay.Idle;
         }
     }
     
     private void BlendSkybox() {
         float temp = 0;
         
         switch(_tod) {
         case TimeOfDay.SunRise:
             temp = (_timeOfDay - sunRise) / _dayCycleInSeconds * skyboxBlendModifier;
             break;
         case TimeOfDay.SunSet:
             temp = (_timeOfDay - sunSet) / _dayCycleInSeconds * skyboxBlendModifier;
             temp = 1 - temp;
             break;
         }
         
         RenderSettings.skybox.SetFloat("_Blend", temp);
     }
 }

So i attached my GameTime script to an empty game object. Then i attached the DontDestroyOnLoad script but it gave me this error when i change the scene: MissingReferenceException: The object of type 'Transform' has been destroyed but you are still trying to access it. Your script should either check if it is null or you should not destroy the object.