Don't know about the temps in Summerdale AL so far, but here in north GA it hasn't been warm enough to heat up any tires, even though we've had some "nice" days.
1. First place I'd start is to check the air pressure in all the tires. THEN check the pressures with a second (new) tire pressure gauge. You may simply not have the right air pressure in the tires. Stranger things have happened. Believe it or don't: tire pressure gauges DO go bad.
2. Mower tires aren't super-duper quality simply because mowers don't achieve life threatening speeds. After a winter of sitting in one place, I'd expect a flat spot on both tires. If you told me you DIDN'T have flat spots, I might have to call you a bad name.
3. The mower is naturally going to want to roll onto the flats when you park. Make sure that doesn't happen when you park. Be brave. Explore new worlds. Flatten a new area on the tires next time you park. See if the tires aren't simply flattening on any area that they sit.
4. Your yard is obviously too small. Next day it turns 80F, ride that mower down to the Morgan County Sheriff's Dept and mow their lawn. Not that tiny patch in front. Oh no, you go mow those 2 acres out back.... between their building and High Street.
If you still have problems (other than being arrested) write again.