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I understand that your main concern is the palpitations you are experiencing in the night.The reasons behind this can be cardiac or non-cardiac. (Related to Heart and un related to heart ).Your Doctor has aptly ruled out thyroid and kidney problems, as both can cause palpitations. Other non cardiac caused include anxiety disorders, REM sleep disorders (since you are having palpitations exclusively in sleep )
I think you would need a detailed electrophysiological analysis (study of the heart if the palpitation). You may need a holter monitoring of your heart. This is essentially recording the ECG for 24 hours a day. Since your problems happens mainly in nights and often unpredictable a 24 hours ECG will give the best results. This is simple test and can be carried out easily. This will help in identifying any rhythm abnormality of heart.
You should avoid napping during day time, taking excessive caffeine (especially before sleep), and smoking – all of this can lead on to sleep disturbance a palpitations.