Too Hot?

Today was our first hot day of the spring in Tennessee (and humid!). It was about 85 degrees F. My eleven-month-old JRT, Gidget, and I went out for our normal afternoon walk, and she seemed to do fine, although she did plop down in the grass and rest for a few minutes which is a first for her (I don't think I've ever seen her lay down on anything but a pillow or furniture before!). On the way home she dragged behind a little bit, and when we got home she had a little drink of water and then headed for the bed to lay down. I was a little concerned so I closed the windows and turned the air conditioning in the house on, and now she seems perky and ready to play again.

I don't think she had heat stroke today, but it's going to get a lot hotter here before the summer is over, so here are my questions. Is an hour too long to walk (briskly) in the summer? Should I take water with me on our walks? Should I be sure to leave the air on in the house for her during the day time? How hot is too hot?? My vet's office told me I could put her in the bathtub with cool water when we got home from walking to cool her down, but that didn't seem like great advice based on reading previous posts to this forum.

Thanks for all of your wonderful advice! It's been such a help to me in raising my JRT.