Checking out flight status on www.cathaypacific.com, and for

CX 807 ORD-HKG on 28 June, there was a note "Please be advised that CX807/28JUN is delayed until 4:10pm local time due to high temperatures in Chicago. Check-in closes at 2:45pm local time. We apologise for any inconvenience caused", and then a re-route to TPE.

So how exactly does temperature play a role in aircraft delays and reroute?

High heat, thin air, less lift, fuel / payload / range restrictions.

Air density decreases with temperature. Warm air is less dense than cold air because there are fewer air molecules in a given volume of warm air than in the same volume of cooler air. As a result, on a hot day, an airplane will require more runway to take off, will have a poor rate of climb and a faster approach and will experience a longer landing roll.

The above will restrict operations on shorter runways. The upshot is increased usage of the longer runways which results in congestion.

This is quite curious. High temperatures can affect an aircrafts take off performance, and could be an issue on an aircraft which is scheduled to depart at Max Take Off Weight. The temperature in Chicago does not appear to be particularly excessive today, although there is some localised thunderstorms.
Would be interested to see what the real issue is.

I'm guessing that CX was unwilling to offload cargo to bring the plane to a reasonable take-off weight.

They must be waiting for a heck of a front to come through and drop air temps by 15F. Normally CHI's high temps at 4:10PM won't be much different from temps at 3:25PM.

Could the purpose of the delay be partially to sort and offload cargo?

I picked up relatives from this flight. Temps in Chicago were no different an hour later (37.2C/99F) when this flight departed. Cathay was quite desperate to offload people from this flight. At check-in they were offering a $400USD voucher, an upgrade voucher, and a rebooking on to the United flight (which they highlighted as "leaving earlier"...although it too was delayed). The comment above regarding unwillingness to offload cargo is probably correct.

The TPE stop was for fuel. The flight circled one revolution while over the coast of Japan (you can actually see this on flightaware.com) which was clearly the moment of decision as to where this flight would go to next. The issue was complicated by Tropical Storm Doksuri in the area. I suspect that the TPE stop was out of safety in case of a lengthy hold upon arrival into HK airspace.

Happens quite a lot with UA's EWR-HKG flight

"The comment above regarding unwillingness to offload cargo is probably correct."

That is not true. As with all other airlines, pax will go before cargo because of higher yield. When the carrier is trying to deny boarding, that means even not carrying any cargo, they are still short of payload.

I'm not an expert in this area - just a layperson - so happy to stand corrected. My impression (perhaps incorrect) from comments by others and CX annual reports was that Cargo had a higher yield than Pax.

Usually they load cargo with yield > pax first + first approx of low yield cargo. and do last min loading if tgeres space. But if there isnt, noones honna take out excess cargo cuz its too late.