I just baked a sponge cake, its sides are fluffy and fine but in the middle it's a bit stiff. When I stick a toothpick in the center it comes out clean and when I cut the cake up, it's not wet. So how should I adjust the baking temperature/time for this case? Thanks!
The very first thing to do is to put an oven thermometer in your oven and find out if your thermostat is accurate. It will take a little while to do this test, because the oven will first overheat then cool then overheat, etc. After 20-30 minutes, you should get a good reading as the interior heats up and the temperatures fluctuations subside. If your reading on the thermometer is different from the t-stat setting, then you will be able to compensate.If it won't hold a steady temp, you should replace the thermostat Sometimes you can recalibrate a home oven t-stat, but it might cost more than it's worth as long as you allow for the discrepancy.
I would not fumble with temperature, as it is important for proper rising. If your cake is too stiff and dry, bake for a shorter time.
If you are getting a very large difference in doneness between sides and center, you will probably have to try to make a more even gradient, like described in this answer about doming. You should also be baking the proper recipe - you can't just pour a bundt optimized recipe into a flat pan and expect it to bake evenly.
But your description sounds a bit strange to me, because you say your middle gets baked through before the sides, which is the opposite of what usually happens. Are you sure your batter is properly mixed? Or maybe your oven has a large hot spot in the middle?