Is it bad for the bike to continuously petal and brake simultaneously (for body heat)?
When it's hot during the day and cold at night, I sometimes find myself under-dressed for late evening riding. I can pedal harder to generate body heat, but on flat ground that creates wind chill & doesn't help. Pedaling hard while lightly holding the brakes works really well to warm up!
But the downhill-biking folks warn about the hazards of overheating brakes (mostly disc brakes but also rim brakes / V-brakes). I have V-brakes.
I imagine just pedaling into brakes transfers heat into them much slowly than controlling downhill descents, since I can go down hills much faster than I can go up hills (it takes much longer to transfer one hill's worth of energy from my muscles into having climbed the hill than to transfer the same one hill's worth of energy into the brakes/rims while descending it).
Just keep a close eye on your brake pads and learn to determine their remaining life. There shouldn’t be any issues unless there are other underlying mechanics issues with the bike. You will not overheat your brakes in a meaningful way just by pedaling.
This process is done intentionally on new bikes (called ‘bedding’ your brakes), although for disk brakes. Bedding rim brakes can have benefits too, like better contact patches.
As others have already said, you will never be able to overheat your brakes this way and brake pads are cheap. My suggestion is that you figure out which brake you wear down quicker (usually the rear for beginners) and use the other one for this. This will make your brakes wear more evenly and prevent having one pair of pads dry out while you wear down the other pair.