I second the suggestion to find the nearest recreational center and take a shower. I’ve done this many a times myself. Or, if there’s no rec center and you have some extra cash, take yourself on a nice night out at a hotel.
I think I’d just bite the bullet. The shock will diminish greatly after a few seconds and you will actually feel very refreshed after you towel off. I’ve been in the situation many times, in places where hot water was a luxury, and the anticipation is worse that the actual experience. Just do it, don’t think it to death.
I keep thinking of what the water at the facet is like here at this time of the year. The water is so cold it cramps my hands.
‘Somebody to Love’ should be OK. It was a Hunter Thompson reference, from Fear and Loathing in Las Vegas. His Attorney wants him to throw a tape player playing that song into the bathtub he’s in.
I don’t know what the big deal was. It was a battery powered tape player.
Bah, I’m with the people saying just heat water in a kettle or something, fill bathroom washbasin and wash that way. I’m sure you will not really get so revolting as to be thrown out of the human race just by not having an actual shower or bath until Monday. And there’s bound to be some neighbour who would let you use the facilities, although, as a “keep myself to myself” person, I do see that one might prefer not to ask the neighbours for favours.
Don’t you work at a university? Universities tend to go in for having sports centres that include showers, and perhaps student halls of residence you could sneak into and “steal” a shower.
BUT, on the other hand, I think you should go up into the loft to relight the thing, because that way you would fall down and get horribly injured and then you would have another good story to tell us. 
The last bit was not meant seriously, folks. There is to be no "Sampiro falls down, goes SPLATT" story. 
For my first six months here in Indonesia, I didn’t have hot water. You just have to suck it up and get under it. It’s easiest if you get your head wet first, then your pits, and finally your balls. Work quickly and efficiently, towel off thoroughly. I also liked to have my morning hot coffee ready when I got out to warm up.
Although if you choose the ‘no-shower no-wash’ option I believe you can mitigate it by liberal use of talcum powder (apply, let it absorb, brush off). And isn’t Alabama warm? Google suggests it’s about 17C in Birmingham at the moment. I know you have a low threshold, but you might still want to consider the old “brisk activity to get the blood flowing followed by a quick cold shower” routine.
Nitpick: It was a battery plus cord model. Raoul Duke threw a 2 lb grapefruit in the bathtub instead, then pulled the cord out of the player so it was on harmless battery power instead, in case his attorney did something stupid. Not that he cared about his attorney, he just didn’t to deal with a dead 300lb Samoan in the bathtub.
Talcum powder? Buy a big bag of fine sand and use if to wash yourself. Nothing cleanses like sand. Mix sand with water in a large bowl until you have a pleasing paste. Put the bowl in sunshine (indoors) for three hours to warm up. Stir frequently. Take the bowl out to the backyard, strip down, and have at 'er. The sun-warmed sand will feel all the warmer if it’s cool outside. Let the sand dry and fall off naturally. Your skin will shine when you’re done. I washed everything with sand when I lived in the desert.
One word: Windex
Top and tails- whore’s bath. Give the undercarriage a bit of a how’s-your-father.
Febreze?
Oh, you city folk! Fill the tub with cold to a depth of about 2 inches. Boil the kettle. Dump the kettle in the water. It’ll probably be too hot - test with your elbow. Add more cold water as required. To get a shower effect for rinsing, use a colander or watering can.
Longer term, look into some kind of woodburning stove or fireplace in case these kind of emergencies happen again.
Depending on the design of your stove, you may not need the pilot in order to light the burner - a lighted match works just as well. That’s part of the fun of gas - in ice storms or other power failures, you can at least cook.
Where my sister lived in rural BC, there were lots of folks who used the woodstove as cooking appliance, water heater, furnace, entertainment centre. The ranch could be without power or phone for weeks at a time, so one just had to be prepared.
I just wanted to say you have my sympathies. I remember well the days when we would run out of propane and have to take freezing showers. We’d just steel ourselves, jump in, soap like lightning, and rinse. The only joy we could take from the situation was to scream throughout, and laugh uneasily at the screams of other household members when it was their turn.
When you step into the shower wash your hands up to your elbow. Then before you can back out duck you head under the spray and let the water run down your back. You will automatically take a deep breath when this happens. But after this initial plunge the water will not seem so cold.
But remember, use newspaper so there won’t be any streaking.