So what about liquid yeast? I ordered some beer supplies last week that included Wyeast 1187 Ringwood ale yeast. The shipment sat in a UPS warehouse all weekend and it arrived today. The ice pack was warm and the yeast was 81 degrees. Will that harm the yeast?
It's a complex combination of the peak temperatures mentioned by Oldpaddy, sustained periods at above-optimal-but-not-lethal temperatures, and variation from strain to strain.
First you have to remember that the ideal temperature for most yeast to grow is around 28-30°C (82-86°F), we only brew at lower temperatures to reduce off-flavours.
You also have to remember that in the wild most yeast survive Mediterranean-type summers in dried form on the bark of a grapevine or fruit tree, waiting for the rain to come that will wash them onto the fruit. So dried yeast are much more hardy than wet yeast, tolerating greater extremes of temperature and losing viability at a much lower rate than wet yeast. In the fridge dry yeast lose viability at a rate of <5% per year, I've made bread with dried bread yeast that spent nearly 20 years at room temperature.
The usual lethal temperatures are quoted as 37°C (99°F) for lager yeast and 42°C (108°F) for ale yeast but that will vary depending on strain. I'd guess eg kolsch yeast will die at 5-10° below the ale norm, whereas saisons will be good for 5-10° higher, and kveik are probably good for who knows, 50°C (122°F)?????? Dry yeast can probably add another 10° or so to the limit for their wet equivalent, and on the other end can survive freezing in a way that wet yeast struggle with.
So your yeast won't have been harmed by being at 81°F in itself, but you have to make a bit of a judgement call on what temperatures it will have been exposed to in its journey to you, if the retailer is in Alaska it will have a different thermal history to a packet sent from Arizona. But you can see why people in the southern US avoid ordering liquid yeast in particular in the summer. We're pretty lucky from that point of view in the UK, in a typical year we only get a week or two at best above 32°C (90°F), but I did delay an order last week because we were in that territory. It's obviously preferable to mostly transport yeast when the temperature is more like say 10°C (50°F). Conversely, you don't want to expose wet yeast to a risk of freezing, so the middle of winter is out.
It also helps to avoid yeast being stuck in depots over the weekend. Obviously it depends a bit on the efficiency of the retailer which you can only figure out by experience (and forum chat) but if they have a quick turnround then the best time to order is on a Sunday so that it's first out the door on Monday and it has the whole working week to get to you. If they're slower then it may be best to order on Thursday or Friday for a Monday/Tuesday dispatch - you soon get to know who is efficient or not.
If you're worried then it's always a good idea to do some kind of starter with liquid yeast, even if it's just a quick vitality starter on the day.