C152 pilot reported radio malfunction during final approach.

Narrative

I'm writing this about the incident that happened with me on final for Runway XXR at ZZZ. I started to experience radio issues when I was 15 NM away from ZZZ. At that time I was under flight following with Center. Center vectored me and got me on 8 NM straight in for Runway XXR and advised me to expect Runway XXR at ZZZ. After which I tried to contact Tower many times by doing 360 before entering the Class D airspace. That was when I heard the Tower say N-number 1 as my radios were barely audible; which made me think that was a clearance for me so I went ahead and landed on Runway XXR because Center had told me to expect Runway XXR. The Tower was also confused with the similar tail number of 2 aircraft and even he released that the aircraft on final was N-number 1 and not N-number 2. And then the Tower asked me to land and contact facilities when I was on final for Runway XXR. After landing the problem continued. I contacted dispatch and Name and after talking for 45mins the radios were some how working for a few minutes; but the radio were heating way too much. I got the clearance to take off from XXR. After leaving the class D airspace I had to turn the radios back OFF as the radio were throwing heat waves and on touching it they felt like they are gonna melt. I had the radios off for the entire flight. I turned them on again when I was 10nm away from ZZZ1. Till the time I landed the radios were heated again.