Your requirements describe the need for a heating pad. Amazon has them for under $20. 20" X 48" for $16 after shipping. Buying a different kind of light to generate heat will be less efficient and surely cost more than a heating pad. I was very hesitant to buy one, but now my seeds germinate super fast. It's worth it.

Not sure about the info on the price of the mat. I do not see anything in this size for that low a price.

On another note. Pre-soaking the seeds would give better results. Soak in some warm water or just use a wet paper towel.

Wet the towel. Should be moist but not dripping.Put some seeds on it. Roll it up and put in a ziploc bag and place on top of your computer or next to the tv. You'll be surprised how much heat your tv generates. Once they sprout, plant them in a light potting soil. Light is the word here. Very well drained.

Also if possible switch the LED with just regular fluorescent bulbs. They give off quite some heat.

Prices change daily. If patient and trying to get the best deal use a price camel like https://camelcamelcamel.com/ and set an alarm on the item your seeking. If anything, it's good to find the best price you can expect and time of year it typically fluctuates towards the lower end. I got my 10 X 20" models when they were $13.

https://camelcamelcamel.com/VIVOSUN-Durable-Waterproof-Seedling-Hydroponic/product/B00P7U259C

Interesting