Yeah, you can use a meat thermometer if it's digital and actually shows the temp.... BUT make sure you clean it WELL after you use it maybe with a bleach and water solution if that wont ruin it. (If you are allowed to stick a meat thermometer in "fish poop soup".... It works but bleh, and some digital meat thermometers can be around 100 bucks... expensive ones, I would not use in my fish tanks personally..... Just thought, some people/fever thermometers are digital, and they come with little plastic bag sleeves so you wouldn't contaminate the thermometer. That might work if you have one?? I think the old school mercury thermometers are hard to find these days.
Another option is to sweat lol. You COULD close the heat/cooler vents in your room and keep the door closed... Not saying this is a pleasant option but it would most likely keep your room warmer. (This may not be an option for your personal well being, just threw it out there. My computer room is where I keep the fish, and it's 82 in here with the air conditioning on. without, its around 90-100... fish stay a good temp but its a bit warm LOL.)
If you can get to a grocery store check out the gift card end caps too. Many stores carry ebay, and pet store gift cards, or the credit card type gift cards you can use anywhere. You can use these online to buy things over the internet often without entering a credit card. Some places require you to add a real credit card though before a purchase anyway, so check the sites you would be interested in purchasing from before you go and buy any cards.
BTW- If your room is 75 your fish water is probably still in the "safe zone" on most fish thermometers but it will be on the very low end. Make sure the tank is NOT by a vent though this will make the water cooler then ambient room temp would be.
I recommend you should probably get a heater of some kind at some point but it shouldn't mean imminent death for the betta. If it takes you a while to get one. (I don't recommend those zoo med round pads because I have one that wants to boil fish. Some users here love those things though.)
I will stress one more time to keep the temp when doing water changes as close as possible to the original tank water though. That is a lot more dangerous then living in cooler water. (If you can gauge the temp pretty close on your finger that will be ok. If you are unsure just acclimate him. OK done stressing my point again! LOL!!!
If you have a meijer by you they might have a cheap heater/thermometer. They often have a really nice selection of pet things. Or a walmart would have a thermometer at the least. They are around 1-4 dollars usually for a glass one that sits in the tank.
As for a good small heater, find out what is best within your price point. I like marina heaters but from the reviews they don't work for everyone. I have 7 of them and all mine work just fine for me. Others hate them because they don't work.
Best of luck to you and your fish. :) Again sorry for my novel long posts. I am the longest winded typer in the forum. :/