Okay, this is an academic question, not really one that will help with the climate-placement goal, but if you were to, say, sail all the way north and then just as you were about to cross over into the southern hemisphere you changed directions, let's say made a right turn, where would you end up? Would it still be in the South Pole region only a little to the right, or would it be, for instance, somewhere in the western sea? Additionally... does a compass always point north in this world such that if you followed it and continued to follow it north you'd end up on a continuous loop passing over the same landmark over and over?

Anyway, so you have seasonal temperature fluctuations just as in the real world, driven by where the sun god decides to travel over the world. (Man, this makes me think up some kind of strange plot where a mad king or wizard or something tries to usurp the sun god to keep the sun stationary over his/her kingdoms or lands to make it alway summer there, not realizing the havoc this causes when the rest of the world is plunged into a sunless ever-winter.)

Now, technically in this flat world you wouldn't have the various effects I described that are caused by a spherical world spinning on its access, but might there by chance be a wind god? Given the existence of a wind god, the winds might not be as static as a flat world might suggest, but might flow in roughly the manner we expect based on observations of the real world. Alternately, the wind god might decide to blow solely from one direction, and this would have vastly different consequeneces for the distribution of climates in your world.

But one thing we know, then, is that where we might, if this was a spherical world, roughly find the tropics and equator, we will have a greater degree of heating of the water and air masses - in the summer more heat toward the northern tropics and in the winter more heat toward the southern tropics. Even without being a spinning globe, we might expect some air and water currents to carry the heat and distribute it outward. Depending on the specific geometry of this world, those currents could flow in any number of unusual directions (would an ocean current flowing off the northwest corner of the world end up in the southeast?)

So... you know what... I should stop and ask: do you want to have a level of detail supporting where you put your climates, or do you want something simple and plausible. If the latter, go with what SG suggested: put them where they are on Earth, and handwave any assumptions about what the gods are doing to make them be there. Having them in realistic places in comparison to where they are on earth lends enough verisimilitude.

If you want to go the detailed route, then my next step would be to start mapping out your ocean and wind currents, deciding as you do whether the ocean and wind gods (assuming such gods exist in this world) are following the same principles in place in the real world or are operating out of some other desire. Even if you get effects similar to what is in place on Earth, the geometry of you world could produce some interesting and unusual climate placements, potentially, depending on how you have everything flowing.