MacBook Pro 2012 13" operating temperature

Hello,

I have a MacBook Pro 2012 with 2,9Ghz i7 CPU and integrated graphics.

I haven't touched it or opened it since I bought it back in 2012.

I saw the last couple of weeks, that the bottom is very warm, and the fan is running high at that point while watching a movie for example. I downloaded an application called Fanny to monitor the temps.

It showed me an idle temperature for the CPU around 65-70 C, and for the GPU 70-75 C.

I assumed it is really warm, and since I haven't done anything to it, time to clean it up a little bit.

I have disassembled it, cleaned out the dust, and replaced the thermal paste.

After reassembling it, to my surprise the idle operating temperature is being shown as 80 C for the CPU and 85 C for the GPU.

I have already reset the SMC and the PRAM, but it did not help.

Have I messed up something? Or is the temperature reading off? Hovewer the fan is not starting, so I assume this temp is not too high, but I have read somewhere that the idle temp should be around 45-50 C.