Yes - the heat can affect your workout that much. To be honest I think you handled it very well. If you think about it this way, there's not a huge difference between 50 degrees and 60 degrees when you are running, but once you pass 80 degrees I think the warmer it gets the worse it is. You are losing a LOT of fluid and electrolytes in a workout like that, especially if it's above 80 degrees. To be honest I don't even like running EASY when it's above 90 degrees but I still do it because I know it's unavoidable. If you are able to, try to plan so you can do a workout in the EARLY am hours before the sun is at full strength. Even though most people typically think noon-1pm is the hottest part of the day, sometimes 3-5 pm can actually be the WORST because at that point the pavement has been soaking up the sun for HOURS and I find that it feels even hotter.
If you absolutely must work out at a time when it's going to be that warm, try splitting up your tempo run into cruise intervals instead. You are receiving the same physiological benefit but it's slightly less stress on your body because you can break up the workout. Also, the idea behind cruise intervals is they are mentally easier but allow you to cover slightly more mileage at quality pace than a straight tempo run does. Jack Daniels explains that you can base your recovery by how many minutes each interval lasts. Since you have been doing a 3 mile tempo run, I would aim for 3-4 miles in cruise intervals (guessing that it will still be hot). For every 5 minutes at tempo pace, you would take 60 seconds rest. So basically for a 1 mile interval you would take 60 seconds.
Two Example Workouts:
3 X 1 mile @ 6:10 pace w/1:00min recovery
OR
2 X 2 mile @ 610 pace w/2:00min recovery
If you feel that you are exceeding tempo effort at this pace I would either slow down slightly and try to focus on achieving tempo effort (listen to your breathing and how your body feels), or...STOP the workout and save it for a better day. It's important to run a workout and do it in an environment where you can achieve the benefits you are working towards. Running your tempo too hard and overstressing your body's ability to use the lactate is going to ruin the purpose of the workout. Also, running in conditions which cause your tempo to go from "Comfortably Hard" to "Painful/Extreme" will also do more harm than good.
Hope this helps..