Theory:

     Next morning, Taro jumped out of bed earlier than usual and made his way to the forest. He chopped and cut, chopped and cut as the sun climbed, and soon he was so warm that he had to take off his jacket. His mouth was dry, and his face was wet with sweat. ‘My poor old father!’ he thought. ‘If only he was as warm as I!’

     And with that he began to chop even faster, thinking of the extra money he must earn to buy the saké to warm the old man’s bones.
Explanation:
  
When the next day came, Taro woke up earlier than usual. He went to the forest to chop wood.
 
forest.jpeg
Forest
  
He kept on chopping and cutting wood. When the sun came out, he started feeling warm. He removed his jacket as it was getting warmer. His face was wet with sweat. He was so thirsty that his mouth was very dry.
 
sweat.png
A man is seen to be sweating due to the hot sun.
 
But he thought about his father and how cold he had felt the previous evening. The word poor in the line 'My poor old father!' refers to the father's sad and unfortunate state. He wasn't bothered by his discomfort or tiredness. All he had wanted to do was to earn more money to buy the saké for his father. He wanted his father to be warm like him. So he was determined to work even harder. He then started chopping the wood faster though he was tired and thirsty.
  
Meanings of the difficult words:
 
Sl. No.
 Words
Meanings
1
Jumped out Getting up quickly.
2
Made his way to Went to.
3
Sun climbedThe sun went up in the sky; it also means that sun is shining well and it is getting hotter.
4
Warm the old man’s bones
Making him feel warm; make him comfortable.
Reference:
National Council of Educational Research and Training (2006). Honeysuckle. Taro’s Reward (pp. 29-34). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.