Laptop shuts down automatically

So my gaming laptop has started getting heating and causes significant fps drops and when playing heavy games the laptop shuts down after 40-45 mins due to overheating, the gpu temps stay around 88-90 rarely reaches 90 and doesn't go above 90 but the cpu temps reach 94-95 and keeps fluctuating between 93-95, the laptop is 1.5 years old and I got th fan cleaned recently but it didn't help at all so should I get the thermal paste and pads replaced or the issue is something else? I inquired about the charges of thermal repaste and pad replacement and they said it would cost 3.5k rupees/ 39.48 usd which i guess is a bit too high? Whats ur suggestion?