Digital sensor arrays based on ring oscillators are used to monitor the temperature of Field Programmable Gate Array (FPGA) chips, but traditional sensor structures using binary frequency counters consume excessive hardware logic resources. This paper proposed a compact temperature sensor array that used low-decoding-complexity linear feedback shift registers (LFSR) as a frequency counter to efficiently count the ring oscillator frequency. We implemented an experimental system on a Spartan-6 FPGA, and the logic resource consumption of the entire system was 927 Look-Up-Tables (LUTs) with an overhead of only 10%. The single sampling time was approximately 40 μs. The proposed temperature sensor array has good temperature sensing capabilities, and the measured error is ±0.9°C(3σ).