Like I said, subbing is simply not an option as I have no way of keeping a specimen warm enough for the hours I'll be at work.
There is a way - handwarmer packs. They are inexpensive and can be purchased at any hunting/camping/sporting goods store.

Ive had many successes with subbing during random situations similar to yours. On one occasion, when I was tapped on the shoulder to go take a U/A, I told the Safety Director that "I left my drivers license at the house and need to go get it (a 20 min drive from the job)".
He grumbled his head off, but he knew: "no picture ID, no test" says the collection facilities policy. So I had him by his gonads and he knew it. So he drove me (with 3 other employees hit with the same random in tow) to the house and that allowed me to microwave my sub to the proper temp.

On another occasion, I had my bottle of synthetic at hand in the facility but had not activated the handwarmer pack. When the collector called out my name and handed me the specimen cup, I walked into the bathroom, activated the handwarmer and attatched it to the bottle. I then walked out and informed the collector that "I could not pee".

Not everybody can urinate on command.

Under DHHS regulations in regards to "shy bladder" situations, the collection facility must allow the donor to sit back in the lobby and drink water for up to 3 hours, or when the donor is able to produce a sufficient amount of sample - whichever comes first. I took advantage of this to allow the handwarmer to heat the synthetic urine to 100F. It took a little more than 1 hour for the bottle to reach 100F, but that was no concern to me because, like Ive stated, I was taking full advantage of the 3-hour window.

The point is that as long as you wont be watched (which you will not on DOT-regulated tests unless youve been suspected of tampering), subbing is an option in random situations. You just have to be a little more creative. When theres a will, theres a way.