Welcome to the forum
Yes guppys can live in cold water but if they have lived in cold water most of their lives i wouldn't advise you move them straight to warm water; what i would do is put them in the new tank or whatever tank they are in and very gradualy raise the temperature over about 2 to 3 weeks so they can adjust let their metabolisms get used to it.
You will find not only will it help extend their lifespans but also they will become more active and you will have more sucess in breeding them. I would say from my experience the ideal tank temp for them would be around 24 to 25 degrees
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Diet wise guppys aern't very demanding, they can happily live off fish flakes their entire lives but they appreciate things live freeze dried daphinia, bloodworms and tubifex every now and then(about once a week, if they are small guppys crushing the food to a certain extent is advised so it is easier for them to eat).
Other than that, there isn't realy much to it; just equip the tank with the usual equipment like a heater, filter and lighting if you decide to have live plants etc.
Just remember when you stock he stock to slightly under stock it so there is room for fry as your guppys will probably breed and to add stock the tank gradually to help avoid water quality problems etc.
Overall your guppys will pretty much look after them selves and will breed with no problem.
Good luck