Have you put a hygrometer or thermometer inside to see if it reads different? Maybe its the probe. This thread has had me curious from the get go lol
It's not that unusual to see temps that high this time of year depending on where he lives. I don't think he mentioned that.
In our old place this time of year in Los Angeles, even with the driver outside the tent, I saw temps hit 97F a couple times during lights on. It really sucked. Generally you'll see the plants get a little stunted, foxtailing and lower buds will be airier than I like.
I don't think I saw lights off temps that extreme though. But growing this time of year can really suck. Seems even harder to get a handle on it in a smaller tent too. YMMV.
If you're running lights on at 1PM and off at 7AM then that 12PM-6PM time slot I have found is the worst. At least where I live. So that is when my lights are off.
I've got a better handle on it in the new place here. Same schedule, but my temps max out at 82F now which I can live with and not have to run the AC like crazy, But we do have central AC here.
One thing I have found is that assuming your exhaust fan is large enough to make a difference, you can run it a little slower to give the (hopefully) cooler air outside the tent some time to actually make a difference in the tent. If you're just sucking air right in and out at the highest possible speed, it doesn't have the time to cool the tent. I run my Infinity exhaust at 4 now.
Or, if you have a temp trigger on your exhaust, set it at 82F to kick in to draw in cool air to cool it down.
I usually size my fan one size larger than the needed size. So for a 4x2, theoretically the needed size would be a 4" fan. I use a 6". In my 4x4 I use an 8".
If all else fails, then it's best to look at the VPD chart posted and get your humidity up to match your temps. Still not ideal. But only so much you can do I suppose.