“What do you give a dog with a fever?”/“Mustard. It’s the best thing for a hot dog.”

Is a dog with a high temperature a “hot” dog? A popular joke is:
 
Q: What do you give a dog with a fever?
A: Mustard. It’s the best thing for a hot dog.
 
The joke was printed in Boys’ Life magazine in February 1981.
 
     
Google Books
February 1981, Boys’ Life, “Think & Grin,” pg. 74, col. 3:
Moe: I think my dog has a fever.
Joe: Go get the mustard.
Moe: Mustard? Why?
Joe: Because it’s the best thing for a hot dog.—Kevin Earl, Delta, Colo.
   
Google Books
Lu & Clancy’s Secret Codes
By Adrienne Mason and Pat Cupples
Toronto, ON: Kids Can Press
1999
Pg. 40:
Joke: What should you give a dog with a fever?
Mustard. It’s the best thing for a hot dog.
     
Google Books
Over 1500 Fantastic Jokes
By Guy Campbell and Paul Moran
London, UK: Dean
2002
Pg. 76:
What do you give a dog with a fever?
Mustard, it’s the best thing for a hot dog!
 
Google Groups: alt.humor.puns
Weakly Jest For Kids 03-02-04
Stan Kegel
3/2/04
(...)
What do you give a dog with a fever? 
Mustard. It’s the best thing for a hot dog!  (Jane, 8)
 
Twitter
Jason Woodmansee
@jasonwoodmansee
Replying to @MicheleRB
@MicheleRB What do you give a dog with a fever? Mustard - that’s the best thing for a hot dog.
12:57 PM - 11 Mar 2009
     
Google Books 
Hot Dog!:
The Wonderful World of the Wiener
By Andy Lynes
London, UK: Pavilion Books Co. Ltd
2015
Pg. ?:
A man goes to the vet because his dog is running a high temperature. The vet takes one look at the panting animal and says, ‘Please wait, I’ll be right back.’ Within moments he returns holding a bottle of French’s. The man, looking puzzled asks, ‘I thought you’d prescribe some pills, what on earth are you going to do with that?’ The vet replies, ‘Everyone knows mustard is the best thing for a hot dog.’
 
Twitter
You Are Joking
@lahlahbean
#mondaymirth
What do you give a dog with a fever?
Mustard, its the best thing for a hot dog!
5:03 AM - 4 Feb 2019