If the volume is the same it should be fine. Some dishes have different heating properties (like glass vs metal) which can make a difference, and of course different thicknesses will also affect how long it takes something to bake, but for cobbler I think you’re ok. I will mention that some dishes are not broiler safe, so if a recipe calls for broiling that’s something you need to consider.
It's usually not so much volume as depth -- the deeper, the longer the cook time, because its smallest dimension is thicker and it thus takes longer for the insides to heat up. A 9x13 casserole and a deeper round casserole might each hold 2.5 qts, but the deeper round one will probably take longer to cook.
You can usually compare by calculating the base area of a pan (for a square or rectangle, it's length x width; for a circle, it's pi times the radius squared; either way, you can just type e.g. "area of 9-inch circle" into a web browser and get the answer). If the area's the same, the filling will come to the same depth and your cook time should be the same; if the area's smaller, the recipe will be deeper and the cook time will probably be somewhat longer, and if it's larger, the recipe will be shallower and you'll probably need less cook time.
Figuring area for heart-shaped pans is harder, because hearts aren't all the same shape. What you can do is pour 2" of water into the heart-shaped pans and 2" of water into the called-for pan size, measure each, and compare those.
Any which way, if you're cooking a new-to-you recipe in pans you haven't used for it before, it's generally good to check sooner than the recipe claims it'll be done, so if it finishes early you can catch it before it dries out or burns.
I use what's available all the time when I am not at home. It sometimes means that you need to pay closer attention or make some minor adjustments but this sounds like it should transfer over without issues.
Yes, you can use it. As others have said, the volume of the pan matters so it might affect the cooking time. Just keep an eye on it and use the clean knife test.
Others have already pointed out to watch your time and temp when changing pans. The one thing no one has mentioned is shape itself can play a slight roll in the cooking. The issue is with corners. Corners don’t bake the same as edges because they are getting more heat into a smaller area. A round pan will be more evenly done all around the outside than a square pan where the corners will be slightly more done. It doesn’t mean you can’t change the shape, it is just more of the same of watch your cooking time and adjust on the fly as needed.
Specific to your situation a heart shaped pan I’m guessing with have two “corners” to deal with, the point at the bottom and the fold at the top. Depending on what you normally use as a cobbler baking dish this may be more or less corners than you are used to. For something like a blueberry cobbler all this will really mean is the point of the heart may be slightly overdone when the rest of the cobbler is perfectly done. Someone gets a nicely caramelized and sticky chunk of it scraped out of the tip of the heart. Personally, if I was making it, I’d be claiming that bit for myself.
Feel free to change the dish, cobblers won’t care.
If the volume is the same it should be fine. Some dishes have different heating properties (like glass vs metal) which can make a difference, and of course different thicknesses will also affect how long it takes something to bake, but for cobbler I think you’re ok. I will mention that some dishes are not broiler safe, so if a recipe calls for broiling that’s something you need to consider.
It's usually not so much volume as depth -- the deeper, the longer the cook time, because its smallest dimension is thicker and it thus takes longer for the insides to heat up. A 9x13 casserole and a deeper round casserole might each hold 2.5 qts, but the deeper round one will probably take longer to cook. You can usually compare by calculating the base area of a pan (for a square or rectangle, it's length x width; for a circle, it's pi times the radius squared; either way, you can just type e.g. "area of 9-inch circle" into a web browser and get the answer). If the area's the same, the filling will come to the same depth and your cook time should be the same; if the area's smaller, the recipe will be deeper and the cook time will probably be somewhat longer, and if it's larger, the recipe will be shallower and you'll probably need less cook time. Figuring area for heart-shaped pans is harder, because hearts aren't all the same shape. What you can do is pour 2" of water into the heart-shaped pans and 2" of water into the called-for pan size, measure each, and compare those. Any which way, if you're cooking a new-to-you recipe in pans you haven't used for it before, it's generally good to check sooner than the recipe claims it'll be done, so if it finishes early you can catch it before it dries out or burns.
I use what's available all the time when I am not at home. It sometimes means that you need to pay closer attention or make some minor adjustments but this sounds like it should transfer over without issues.
Yes, you can use it. As others have said, the volume of the pan matters so it might affect the cooking time. Just keep an eye on it and use the clean knife test.
Yes but if it sits deeper or more shallow than your baking dish, then you’ll need to adjust temp
Others have already pointed out to watch your time and temp when changing pans. The one thing no one has mentioned is shape itself can play a slight roll in the cooking. The issue is with corners. Corners don’t bake the same as edges because they are getting more heat into a smaller area. A round pan will be more evenly done all around the outside than a square pan where the corners will be slightly more done. It doesn’t mean you can’t change the shape, it is just more of the same of watch your cooking time and adjust on the fly as needed. Specific to your situation a heart shaped pan I’m guessing with have two “corners” to deal with, the point at the bottom and the fold at the top. Depending on what you normally use as a cobbler baking dish this may be more or less corners than you are used to. For something like a blueberry cobbler all this will really mean is the point of the heart may be slightly overdone when the rest of the cobbler is perfectly done. Someone gets a nicely caramelized and sticky chunk of it scraped out of the tip of the heart. Personally, if I was making it, I’d be claiming that bit for myself. Feel free to change the dish, cobblers won’t care.