What does the Amp rating on a Diode Mean?
The key is to read the datasheet carefully. The 1A or whatever rating is under some particular set of conditions that may be optimistic for your situation. In the case of the 1N4007 (what I assume you mean, since a 1N1007 is an old germanium diode) a "1A" rectifier, the rating is specified as follows: 



So we are talking average rectified output current with the lead temperature maintained at 75°C 9.5mm from the case. Note that they effectively define this as the ambient temperature which is.. rather dubious. There is an obvious danger if you have long leads and are running close to the maximum current. On the plus side, the actual RMS current may be significantly higher than the average rectified output current. 

A graph on the datasheet shows linear derating to zero at 150°C (again that's the lead temperature 9.5mm from the case). 

If you are running at higher current (or even close to 1A) I suggest you use a higher rated part such as 1N5407 or a Schottky 3A diode which would run cooler (because less voltage drop) eg. 1N5821. The 1N5821 datasheet I linked is a bit more honest in that it refers to Tl (lead temperature) rather than ambient temperature, however it is specifically the cathode lead and only 1/32" (0.8mm) from the case! There is detailed thermal design material in that datasheet, and it's pretty straightforward, just simple arithmetic. 

Of course if your adapter can supply 2A but you are sure your load can never draw more than (say) 0.5A then a 1A diode is fine.