Mine has gone as high as 93° 77% when the outside temps are in the 90s. I watch my leaves like a hawk, its the first indicator to how your plants are reacting to changing conditions. The leaves can get a little edgy when it goes that high, i usually just pull my lights up a little, maybe dim them 10%. When it drops out of that high range the leafs start to sag a little so i try to bring the heat up, 1st by turning the light intensity up or lowering the light closer to the canopy, if that's not enough i kick on the heater.
HID is fine for you if those are your lights on temps and not just how hot it gets in there during the day with the lights off. I was just kidding about led, im a convert and i think everybody should convert for a lot of good reasons but it can be cost prohibitive. Youll get really good leaf surface temps with hps, just have to keep the other parameters in check. Its the interplay of temp, humidity and light intensity that make it safe to grow in those temps. Look up some vpd charts and they will show you the safe ranges for most temps under 95°. The only thing they dont help with is light intensity, you kind of have to play with that on your own.