Organic hole transport layers (HTLs) have been known to be susceptible to thermal stress, leading to poor long-term stability in perovskite solar cells (PSCs). We synthesized three 2,5-dialkoxy-substituted, 1,4-bis(2-thienyl)phenylene (TPT)-based conjugated polymers (CPs) linked with thiophene-based (thiophene (T) and thienothiophene (TT)) comonomers and evaluated them as HTLs in n-i-p PSCs. TPT-T (MB/C6), which has branched 2-methylbutyl and linear hexyl (MB/C6) side chains, emerged as a promising HTL candidate, enabling power conversion efficiencies (PCEs) greater than 15%. In addition, PSCs with this HTL showed an improvement in long-term stability at elevated temperatures of 65 °C when compared to those with the state-of-art HTL, 2,2',7,7'-tetrakis(-dimethoxyphenylamino)-9,9'-spirobifluorene (spiro-OMeTAD). This improvement is ascribed to the lack of thermal transitions within the operational temperature range of PSCs for TPT-T (MB/C6), which is attributed to the relatively short branched side chains of this polymer. We propose that the elimination of thermal transitions below 200 °C leads to HTLs without cracking as-deposited and after conducting a stress test at 65 °C, which can serve as a new design guideline for HTL development.