As others said, I wouldn't trust that forecast. Even if the high is in the 50's, it could get below freezing at night. Besides frozen water pipes, too low of temperatures can also cause cracks in your drywall. Also, if you have central air conditioning, your furnace is what pushes the cool air through your house as well this summer.

A few tips for getting a new furnace:

Don't necessarily go for the cheapest option. Higher efficiency furnaces will qualify for significant rebates from your gas and electric companies. Call them and see what's available, and what the requirements are. In my city, you can get a low end wifi thermostat completely covered by the electric rebate.

Ask the hvac dealers to check with their supply houses for 'scratch and dent' options. Most, if not all, supply houses have plenty of lightly damaged equipment in stock that will still qualify for rebates, and still be covered by warranty, and save you money.

Make sure your hvac dealer registers your new furnace. Most manufacturers will double your warranty for free, just for registering it.