I have transplanted roses in arid triple digit temps. I know people who have transplanted them in desert climates in mid-summer. In other words, it's doable.
The fact that you are in your rainy season really makes it easier than it would be for me doing it in my dry summer season because the biggest problem for me is having the canes dry out.
However, I have never grown roses in a humid climate, so I can only guess that your issues are completely different than mine.
Generally, when we transplant a rose or put a rose in the ground, we damage the feeder roots and we are told to water the plant daily because the root system is inefficient until the rose grows new feeder roots. If the soil is too wet, those new feeder roots will rot and the rose will not take off. It's not the heat that is going to kill the rose, it's the inefficient root system that is going to cause the rose to fail. So, if you think your soil will be too wet to plant it out now and you think the roses are too stressed by being in gallon sized containers, maybe the best solution is to pot them up to larger containers and give them more room for their roots until you think it's a better time to plant them out into the garden.
I know that means handling them twice, but it really is a judgment call on your part because you know your climate and your soil conditions.
I had one rose this year that I kept too long in a container that was too small before getting it planted out because every spot I thought I wanted to plant it ended up having severe root competition. I should have potted the rose up and waited until fall to plant it out. Unfortunately, my high summer temps arrived two weeks early and I had just gotten the plant into the ground. I've had to give that rose a LOT of TLC and it's doing fine even in triple digit temps, but I am watching it closely. I don't have to worry about the soil being too wet or about drainage, but I do have to make certain that the top growth doesn't fry because of the low humidity in my garden and the root system is inefficient at this stage.
In both cases, it's all about how the roots are developing as the plant is settling in to its new location, not about the heat.