Bill's right about the incision area. Chlorine might not do it much good either, before it heals up.
A regular bath cools as you lay in it. A hot tub maintains temp. Heat over time is the variable component.
The thing that occurs to me is that I generally feel good, but drained of energy when I climb out. Early on, I would be cautious about overdoing it. I don't have any valid reason to believe that it would actually be a problem. It's just the way it strikes me.
If your cardio says no hot tub, even after the incision heals, ask your surgeon as well. My cardio told me not to fly this summer. Plenty of people on this site were on planes a week after surgery. Were they taking a risk, or is he full of beans? What I'm saying is just that there is frequently more than one valid, professional opinion of these things.
Best wishes,