Chicken wire is fine. I put chicken wire over some of my plants (flowers, young bushes, etc...), and my summers almost reach 110'F and haven't noticed any issue related to heat and etc...
The only issue I've had is if a
fruit tree's branch moves back and forth in the wind and rubs some of its own bark off on the wire, but I haven't had issues with my young bushes *growing through* the chicken wire.
Also
bear in mind many people use metal
trellis for their
tomatoes, raspberries, blackberries, etc... last year, I had pumpkins and squashes trellis'd (again, nearly 110'F some days) - no problem with the heat of the wire itself - at least that I noticed. The plants did struggle with the heat in-general, but then again, so did I. =P
As one last note, if the flowers grow through the wires, they'll be shading the wire - at least the parts nearest them.