I buy all my livestock from local lfs's ranging from 20 minute-1.5 hour drive away ,got some stylorofoam boxes I take to lfs with me ( they usually give you one if you buying a few things and ask them) so as I won't buy livestock online and drive hone not so far,the temp in bag not so bad I would of guessed ( never checked )
For corals I float bag in sump with low light from cheap led strips for 15-20 minutes for temp acliminastion ,then dip and swoosh/turkey baster them for pests then straight into dt,read many times and watched lots videos saying corals self aclimintise ( not sure scientific name) so no need to drip corals.
For fish I float 15-20 minutes in sump for temp acliminasation and leave open bag and use peg to clip to side of sump and start a drip going from main dt with airline tubing with a couple of knots in tubing to slow drips down,like 1 every second or so and every 10 minutes use cup and scoop some water out bag and keep doing this for 30-45 minutes.
If buy fish online ,using drip method can be deadly for the fish as amnonia rises in the bag and fish breathes and stuff the ph drops so amnonia not so toxic but when open bag the ph rises and amnonia becomes more toxic and could be deadly so need to bare this in mind ( google amnonia in fish shipping bag and how to acliminate and be more precise explanation and process)
For inverts I float bag in sump for 15-20 minutes for temp acliminasation and open bag and peg to side of tank and drip acliminate same as above with fish buy generally do little longer ,like 45 minutes -1 hour.
Reason for opening bag and leaving livestock in bag in sump while drip aclimitise is the temp stays stable as if float bag first then move livestock to say a bucket and start a drip acliminasation for 30 minutes or upto 2 hours like you mentioned ,unless you got a heater in that bucket I wouldn't be confident tje water stay correct temp and if temp falls in this time then makes pointless you floating bag at begginning for temp acliminasation ,I read some say as water dripping in,its putting correct temp water in bucket so all ok,but I would expect as it dripping so slowly and no heater ,it's going to lose temperature ( depending temp of room off course ) but could just float a thermoter in bucket to check and add a heater if needed .
I just find it easier to leave open bag clipped to side of sump glass,but keep eye on it as dont want lfs bag water to overflow into your sump or dt whichever you using .
Goodluck