Wheater said with a smile: "I trained with him every week, so I know how to handle him."
Boro boss Gareth Southgate said: "When we talk about setbacks at clubs, we always focus on the negative of it.
"But for getting those opportunities with us, he would not have been an Under-21 international this week.
"It is fantastic for him and fantastic for the club that he and Adam Johnson have become two more Under-21 internationals. That is great credit again to the academy.
"We hope David can continue to play the way he has been because he has been outstanding."
With Woodgate now nearing his return, Wheater knows he will have to maintain his level of performance if he is to hold on to his place, but he is relishing his big chance.
He said: "I am really enjoying it. It's bad that it came from all the injuries to my mates, but I took the chance when I had it, so it has been good.
"The first friendly we had, I don't think I was starting, then the day before, Chris Riggott got injured and I have just taken my chance from there.
"It is going to be tough, but hopefully I have played well enough and will keep playing well enough to keep my place."