In the GLEX, we have emergency pressurization just as in the LR. It would only come into play until both packs are inop, both channels on both pressurization controllers were inop and operation above 10,000 were absolutely necessary. From the testing, I understand cabin temp will stablize at around 85-90 degrees F at flight levels. Bearable, but uncomfortable.
In the Lear 35, the temperature goes up substantially; it gets very hot, and also loud. The lear doesn't have a "pack" per se, but a cooling system comprised of a hot air bypass valve and flow valve, along with a heat exchanger. It's not really a pack, and there's no ACM. Some aircraft are equipped with freon air conditioning.